# Effect of forming strategies on strain paths and local strain evolution in incremental sheet forming using digital image correlation

Raphaël Le Franc, Ahmad Al Khatib, Jean-François Coulon, Jean-Benoit Le Cam, Gwenael Picaut

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Raphaël Le Franc, Ahmad Al Khatib, Jean-François Coulon, Jean-Benoit Le Cam, Gwenael Picaut. Effect of forming strategies on strain paths and local strain evolution in incremental sheet forming using digital image correlation. 28th European Scientific Association for Material Forming International Conference-ESAFORM-Annual, May 2025, Paestum, Italy. 10.21741/9781644903599-132. hal-05421779

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# Effect of forming strategies on strain paths and local strain evolution in incremental sheet forming using digital image correlation

Raphaël LE FRANC¹,ª, Ahmad AL KHATIB²,ᵇ, Jean-François COULON²,ᶜ, Jean-Benoît LE CAM³,ᵈ, Gwenaël PICAUT⁵,ᵉ

¹HALCYON, 7 Rue des Couardières, 35136, Saint-Jacques-de-la-Lande, France

²ECAM Louis de Broglie, Campus de Ker-Lann, 2 Ctr Antoine de Saint-Exupéry, 35170 Bruz, France

³Université de Rennes, Institut de Physique de Rennes, UMR 6251 CNRS/Université de Rennes, Campus de Beaulieu, Bât. 10B, 35042 Rennes Cedex, France

ªraphael.le-franc@halcyon-performance.com, ᵇahmad.al-khatib@ecam-rennes.fr,

ᶜjean-francois.coulon@ecam-rennes.fr, ᵈjean-benoit.lecam@univ-rennes1.fr,

ᵉgwenael.picaut@halcyon-performance.com

**Keywords:** Incremental Sheet Forming, Digital Image Correlation, Strain Evolution, Strain Path, Forming Limit Curves at Fracture

**Abstract.** Incremental sheet forming (ISF) is widely used for prototyping and small-batch production due to its flexibility and cost efficiency, particularly in the aeronautics and aerospace industries. Unlike traditional stamping, ISF uses a single hemispherical tool mounted on a robot or Computer Numerical Control (CNC) machine, which induces complex strain paths and higher formability. This necessitates a deeper understanding of deformation mechanisms to accurately define forming limits of this process. The aim of this paper is to study the strain path and local strain evolution in the ISF of AA2024-O aluminium alloy sheets and to investigate the influence of forming strategy on these strains. To achieve this, a novel method is employed by combining the wing stars test with the Digital Image Correlation (DIC) technique. The wing stars test, commonly used to characterize the Forming Limit Curve at Fracture (FLCF), is used to create a two-wing star (TWS) shape, inducing strain paths between equibiaxial strain and plane strain. DIC is utilized to capture surface strain on the sheet during the forming process, enhancing our understanding of deformation mechanisms. Strain paths and local strain evolution in different zones of the sheet during the tool's pass are captured for three forming strategies. These strategies involve a cycle of four upward and downward tool passes, each with a fixed ΔZ per pass. The results demonstrate differences in strain paths in the zones near the wall of the TWS for the three strategies. Additionally, strain patterns for each strain component are identified in each zone of the TWS shape after the tool pass. The aim of this work is to understand the deformation mechanisms of the two-wingstar (TWS) geometry in order to reliably extract and control the evolution of deformation paths. This will enable the implementation of this test as a characterization method for incremental forming within industrial context.

**Introduction**

Single Point Incremental Forming (SPIF) is an innovative sheet metal forming process that has garnered increasing attention for its applications in prototyping and small batch production: especially in aeronautics and aerospace [1]. This technique involves the progressive shaping of a metal sheet using a displacement-controlled hemispherical tool, which eliminates the need for a supporting die [2]. This forming process, characterized by its high flexibility, cost efficiency, and enhanced forming limits, represents a significant technological advancement in manufacturing sheet metal parts compared to traditional drawing processes [3], [4]. The contact between the tool

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and the sheet results in an isolated strain path compared to the traditional deep drawing process. This is attributed to the fact that the deformed zone is confined exclusively to the contact region between the tool and the workpiece [5]. However, despite these advantages, challenges such as shape inaccuracy due to the springback effect [6], the heterogeneous distribution of thickness strains [7], and the prolonged fabrication time have been reported, which can limit the process.

Formability in SPIF has been extensively investigated in numerous studies [4], [8], [9], [10]. It is typically characterized by the draw angle $Φ$ or the draw angle $α$ (Fig. 1), which is defined by the sine law: $t_f = t_0\sin(\frac{\pi}{2} - \Phi) = t_0\sin(\alpha)$ (see Fig. 1), where $t_0$ represents the initial sheet thickness and $t_f$ the final sheet thickness. The maximum design draw angle $Φ$ of the part must be less than $Φ_{max}$, which can be considered as a material parameter limit [2]. Moreover, the Forming Limit Diagrams (FLD) used typically in conventional press forming, is employed in SPIF to define the strain limitation in the principal strain space ($ε_{major}$ and $ε_{minor}$ or $ε_1$ and $ε_2$). The conventional Forming Limit Curve (FLC) describes the relationship between the major and minor strains in the sheet plane at the onset of necking failure. These strain values are obtained through a series of experiments conducted under various loading conditions, ranging from biaxial tension (stretch forming) to balanced tension and compression (deep drawing) [11]. However, unlike the FLD of conventional forming process which characterized by the onset of localized necking based on principal strain conditions, SPIF process is predominantly constrained by fracture with localized necking effectively suppressed [12]. The Fracture Forming Limit (FFL) (see Fig. 2) observed in the ISF process demonstrates significantly higher strain levels compared to the conventional Forming Limit Diagram (FLD) [2], [5], [13], [14]. Experimental, theoretical, and numerical analyses have confirmed that FFL curves effectively capture the fracture behavior in SPIF, accounting for the diverse strain paths encountered during the process [15], [16], [17], [18], [19]. This distinction can be attributed to the localized deformation mechanisms inherent to the process and the unique strain paths they generate. Common tests for generating forming limits curves in incremental forming include Nakajima tests, dome tests, and bulge tests [20], [21], [22]. Still, these techniques do not accurately represent strain mechanisms in ISF, where the fracture occurs without necking. Another characterizing test for FLCF, called wing stars test, is proposed by some works [23]. It consists of generating three strain paths by SPIF tool by producing three shapes out and two wing stars and a truncated pyramidal shape. This offers advantages such as: a) simple implementation using ISF equipment, and b) similar load conditions, tool contact, and strain paths as ISF. These advantages enable also strain field analysis from the Digital Image Correlation (DIC) technique to improve the understanding of deformation mechanisms and consequently optimize the process conditions.

<figure><img src="image_3.png" /><figcaption>Figure 1 – Schematic diagram of ISF process.</figcaption></figure>

Numerous studies have sought to investigate the deformation mechanics underlying Single Point Incremental Forming (SPIF) to gain a deeper understanding of how process parameters, such as toolpath and forming strategy, influence formability and geometric accuracy of the part. One prominent conclusion is that the average stress triaxiality in SPIF is significantly lower than in conventional forming processes, thereby explaining its superior formability [24]. Furthermore,
other studies have reported the coexistence of stretching, bending, and shearing deformations during SPIF [25], [26]. In addition, research on the Double-Sided Incremental Forming (DSIF) process has revealed that the primary deformation modes in both single-pass and reforming scenarios include plane strain tension, plane strain compression, and shear. These modes are strongly influenced by tool positioning and exhibit significant variations across the sheet surface [27]. These studies underscore the importance of understanding local strain phenomena as a prerequisite for generalizing deformation behaviour across the entire process, through experiments and finite element models. In many instances, ISF does not adhere to a single strain path; instead, multiple passes at the same location on the sheet often occur. Moreover, ISF process can include many forming strategies defined by multiple forming tool passes. However, little is known about the impact of such multi-passes forming strategies on strain paths and local strain evolutions of the formed shape.

This study aims to investigate the strain mechanisms in Single Point Incremental Forming (SPIF) by analyzing strain paths and the local strain evolution during the forming of AA2024-O aluminum alloy sheets. By employing various forming strategies, this research seeks to gain deeper insights into the key factors influencing strain path evolution. To achieve this, the wing stars characterization method is employed to produce Two-Wing Stars (TWS) shapes designed to create strain paths between equibiaxial strain and plane strain. The process involves repeated upward and downward movements of the forming tool with a constant step increment of $\Delta z = 0.2$ mm. Three forming strategies, defined by combinations of upward and downward tool passes, are tested: DUDU (Down-Up-Down-Up), UUDU (Up-Up-Down-Up), and UDDU (Up-Down-Down-Up). The TWS test is combined with 3D Digital Image Correlation (DIC) to measure the surface strain field of the formed shape throughout the forming process. Based on DIC measurements, strain paths are plotted in the FFL diagrams for five zones of the formed surface.

In the first section the experimental setup used in this study, including ISF and 3D-DIC equipment, is presented. Section 2 analyzes and discusses the results of the full kinematic strain field measurements in principal strain space for the three forming strategies. Finally, Section 3 provides the conclusions and future perspectives.

## Experiments

Experimental SPIF setup, tool path trajectory, and tool path strategies. The SPIF process was applied to the aluminum alloy sheet to form the first geometry, the "Two-Winstar Shape (TWS)," from the characterization method proposed by [8], aimed at determining the Forming Limit Diagram (FLD) for the SPIF process. This geometry is designed to induce a strain path on the sheet that transitions in-between equibiaxial strain and plane strain.

In this study, the TWS geometry is formed using an adapted three-axis CNC milling machine (SBC), which was modified by incorporating a fixed fourth axis for incremental forming. A welded structure was developed to rotate the specimen by 90° relative to the machine's initial horizontal plane, thereby providing the necessary clearance for the 3D digital image correlation (3D-DIC) system. The forming setup is illustrated in Fig. 2.

The initial sheet specimen, measuring 160 × 60 mm, was fixed between the die (positioned beneath the sheet) and the blank holder (above the sheet). Both the die and blank holder were machined from aluminum alloy plates. The sheet is formed using a 20 mm diameter hemispherical tool, operating at a constant speed of 2 m/min. During the forming process, the tool follows predefined paths from point A to point B, repeating with an increment of $\Delta Z = 0.2$ mm, as depicted in Fig. 3.

To study the influence of different forming strategies and the impact of multiple passes on sheet strain, three distinct strategies were employed to produce the same TWS geometry (refer to Fig. 4). These strategies are designated as follows: DUDU (Down-Up-Down-Up), UUDU (Down-Up-Down-Down), and UDDU (Down-Up-Up-Down). Each strategy consists of repeated cycles of
Down and Up tool paths, where Down indicates tool movement in the X-axis direction and Up refers to movement opposite to the X-axis. For each Down or Up movement, a downward increment of $\Delta Z = 0.2$ mm was applied.

<figure><img src="image_4.png" /><figcaption>Figure 2 – Instrumentation setup for incremental sheet forming.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 3 – Forming side and DIC side of the setup.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 4 – Forming tool and tool path definition for incremental sheet forming.</figcaption></figure>

## Results and discussions

Analysis of the evolution of the principal strain field using full kinematic field measurements. To analyze the strain paths in various regions of the formed sheet, five distinct zones C0, C1, C2, C3, and C4 are defined, as shown in Fig. 5. Fig. 5 also provides cross-sectional views of the deformed sheet with the forming tool, offering a clearer representation of the relative positions of these zones. These zones are strategically selected to capture the local strain variations in the deformation area of the sheet for the three forming strategies of SPIF process: DUDU, UUDU, and UDDU, as outlined earlier.

For each strategy, the complete forming process is recorded through a synchronized acquisition of image pairs at 4 Hz, resulting in a total of 1646 pairs of images. The overall dimensions of the produced TWS geometry are 140 × 40 mm for the three strategies.
Fig. 6 shows strain paths for the zones of interest: C0, C1, C2, C3, and C4 of the formed TWS shape for the first strategy DUDU. They are represented by the evolution of major strains (y-axis) and minor strains (x-axis) in the principal strain space. This representation, commonly used in conventional press forming, visualizes the material's safe forming space in terms of principal strain conditions for the onset of necking. In Incremental Sheet Forming (ISF), however, the safe forming space differs due to the suppression of necking. Consequently, the Forming Limit Curve at Fracture (FLCF) in ISF exhibits significantly higher strain levels compared to the classical Forming Limit Diagram (FLD) [28].

As shown in Fig. 6, the strain field within the formed sheet is heterogeneous, consisting of multiple deformation stages within a single zone caused by the repeated passes of the forming tool. The strain path and amplitude vary across the zones of interest. While all zones (C0 to C4) exhibit biaxial stretching strain paths, the slopes differ between them. The biaxiality coefficient ($\beta = \frac{\epsilon_{minor}}{\epsilon_{major}}$) – a parameter describing the relationship between strains in two principal directions – further highlights these variations: $\beta_{C0} = 0.198$, $\beta_{C1} = 0.107$, $\beta_{C2} = 0.112$, $\beta_{C3} = 0.075$ and $\beta_{C4} = 0.094$.

This variation confirms that the strain paths are non-uniform, resulting in a heterogeneous kinematic strain field. Notably, the highest deformation occurs at C0, aligning with its designation as the fracture zone. For the other zones (C1, C2, C3, and C4), the strain paths are expected to be symmetric relative to the length of the TWS shape. However, slight variation is observed when comparing C1 with C2 or C3 with C4. These findings also hold true for the UDDU and UUDU strategies, as discussed in the following section.

These findings emphasize the localized nature of deformation in ISF, showcasing its distinct characteristics compared to traditional forming processes.

<figure><img src="image_7.png" /><figcaption>Figure 5 – Areas of interest C0, C1, C2, C3, and C4, and cross-sectional views of the position of these points on a 3D model.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 6 - Strain path for zones of interest C0, C2, C3, C3, and C4 for DUDU strategy, and biaxiality coefficient ($\beta_x$).</figcaption></figure>

Effect of forming strategy on the heterogeneity of the principal strain field. The strain paths of the identified zones of interest are compared across three forming strategies (DUDU, UUDU, and UDDU) to evaluate the impact of the forming strategy on the strain field of the TWS shape in Fig. 7 to 12. The DUDU strategy serves as the reference approach, as employed in [23]. The objective of the UUDU strategy is to investigate the effect of incorporating additional upward passes, while the UDDU strategy aims to assess the impact of increasing the number of downward passes. Each figure plots the strain paths for one zone of interest for the three forming strategies in the principal strain space. The scales have been rescaled to better show the differences between the strategies.

In Fig. 7, at zone C0, no significant differences are observed in either the biaxiality coefficient or the strain amplitude across the different strategies. The biaxiality coefficient ranges from 0.192 for the UDDU strategy to 0.198 for both the DUDU and UUDU strategies, indicating that the deformation mode remains the same regardless of the strategy employed. The maximum strain remains relatively consistent regardless of the forming strategy too, with minimal variation. The major strain values at C0 are approximately 0.656 for the UUDU strategy, 0.665 for the DUDU strategy, and 0.641 for the UDDU strategy. These results indicate that strain path and the fracture limit at zone C0 is not influenced significantly by the used forming strategy.

<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /><figcaption>Figure 7 – Strain path for the area of interest C0, C1, C2, C3, and C4 for DUDU, UUDU, and UDDU strategies.</figcaption></figure>

By analyzing the strain levels in the zones at C1, C2, C3, and C4 near the wall for the three strategies, it becomes evident that the strain amplitude varies across these zones depending on the tool path strategy. The strategy DUDU always has the most important strain amplitude compared to other strategies for the zones C1, C2, C3 and C4.

The strain amplitude in zones C2 is higher in the UDDU strategy compared to the UUDU strategy. On the other hand, zones C3 and C4 exhibit greater strain levels in the UUDU strategy than in the UDDU strategy.

Additionally, as shown in Fig. 7 to 12, the biaxiality coefficient remains relatively consistent, with slight variations observed among the three strategies, particularly in zones C1 and C2. A comparison of the strain paths for C1 and C2, as well as C3 and C4, suggests a near-symmetric deformation mode along the length of the part, indicating that both halves of the part undergo similar deformation. This symmetry is logical and expected, given the hemispherical geometry of the tool.

This observation suggests that the forming strategy significantly affects the strain path, particularly the strain amplitude. Further investigation is required to better understand this influence, focusing on the analysis of local deformation in the sheet and the interaction between the tool and the sheet material.

Due to these findings, the right half part only – areas C0, C2, and C4 – will be considered for further analysis in future work.
## Conclusion

This study provided an in-depth investigation of the principal strain components to elucidate the strain field heterogeneity in the TWS geometry under various tool path strategies during the SPIF process. Using 3D Digital Image Correlation (DIC) and Vic3D software, the strain distribution in AA2024-O aluminum sheets was analyzed with high precision. The results revealed that the geometry of the TWS induces a heterogeneous strain field due to its shape and the localized tool/sheet contact. Notably, the tool impacts the material beyond its direct contact areas, demonstrating an indirect influence on the entire part.

The analysis highlighted distinct deformation behaviors between the upper and lower sections of the TWS, depending on the tool path strategy. The upper section experienced greater deformation in terms of principal strain components during upward passes, while the lower section showed higher deformation during downward passes. In contrast, the strain behavior near the forming wall zones (C1 to C4) exhibited an inverse trend, with C0, the part's tip, remaining unaffected by the tool path strategy. Furthermore, strain path analysis revealed that the regions C1 to C4 predominantly followed a plane strain mode, whereas C0 clearly exhibited a biaxial strain mode.

To further explore these findings, future work will involve a detailed analysis of the strain components $ε_{xx}$, $ε_{yy}$, and $ε_{xy}$ to provide deeper insights into the strain mechanisms governing different zones of the TWS geometry. This will contribute to a more comprehensive understanding of the deformation behavior in SPIF and support the optimization of forming strategies for industrial applications. Additionally, further strategies need to be developed to examine the influence of the sequencing of upward and downward passes.

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