The strain compensation method for measuring in-plane forming limit curves (FLCs) using 2D digital image correlation developed previously [A method of measuring in-plane forming limit curves using 2D Digital Image Correlation, SAE Int. J. Mater. Manf., 2023] was modified and extended to more versatile and popular out-of-plane FLCs. The current study introduces a straightforward strain compensation technique for measuring Nakazima testing based out-of-plane FLCs utilizing an affordable single-camera (2D) DIC system. In this study, forming tests are performed on two automotive-grade sheet metal alloys: DP980 steel and a 6xxx series aluminum alloy using the Nakazima test method. The experiments are conducted on a customized setup that allows for simultaneous optical strain measurements using both a stereo DIC and a 2D DIC system. The FLCs are obtained by applying a temporal FLC computation approach to the two measurement sets. The results show that 2D DIC FLC points match those obtained by stereo DIC for both the materials after applying the proposed strain correction method.
Citation: Agha, A., & Abu-Farha, F. (2023). On the
Measurement of Nakazima Testing Based Out-of-Plane Forming Limit
Curves using 2D Digital Image Correlation. International Journal
of Pioneering Technology and Engineering, 2(01), 120-127.
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With the introduction of advanced lightweight materials with
complex microstructures and behaviors, more focus is put on the
accurate determination of their forming limits, and that can only
be possible through experiments, as the conventional theoretical
models for forming limiting curve (FLC) prediction fail to
perform. Despite that, CAE engineers, designers, and tool makers
still rely heavily on theoretical models due to the steep costs
associated with formability testing, including mechanical setup, a
large number of tests, and the cost of a stereo digital image
correlation (DIC) system.
The International Standard ISO 12004-2:2021 recommends using a stereo DIC system for formability testing since 2D DIC systems are considered incapable of producing reliable strains due to errors associated with out-of-plane motion and deformation. This work challenges that notion and proposes a simple strain compensation method for the determination of FLCs using a low-cost single camera (2D) DIC system.
In this study, formability tests are performed on an automotive-grade 6xxx series aluminum alloy using the Marciniak in-plane FLC testing method. The tests are performed on a custom setup that enables simultaneous optical strain measurements using a stereo DIC as well as a 2D DIC system. The results show how 2D DIC FLC points match those obtained by stereo DIC using two popular FLC approaches: ISO 12004-2 section-based spatial method and a time-dependent Linear Best Fit (LBF) method.
Citation: Agha, A., and Abu-Farha, F., "A Method for
Measuring In-Plane Forming Limit Curves (FLC) using 2D Digital
Image Correlation," SAE MobilityRxiv™ Preprint, submitted February
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It is a consensus in academia and the industry that 2D Digital
Image Correlation (2D-DIC) is inferior to a stereo DIC for
high-accuracy material testing applications. It has been
theoretically established by previous researchers that the 2D-DIC
measurements are prone to errors due to the inability of the
technique to capture the out-of-plane motion/rotation and the
calibration errors due to lens distortion. Despite these flaws,
2D-DIC is still widely used in several applications involving high
accuracy and precision, for example- studying the fracture
behavior of sheet metal alloys. It is, therefore, necessary to
understand and quantify the measurement errors induced in the
In this light, the presented work attempts to evaluate the effectiveness of 2D-DIC in mechanical testing required for the generation of fracture strain vs. triaxiality curve for sheet metal. This work presents a direct comparison of fracture strains obtained by 2D-DIC and stereo DIC for four loading conditions (uniaxial tension, plane strain, shear, and balanced biaxial tension) on two materials with very diverse mechanical and fracture properties - CR4 and DP800 steel.
The comparisons are done for full-field strain contours, fracture strains and strain paths/triaxialities generated using the two DIC systems. A simple technique is proposed to compensate for the effects of out-of-plane motion in the 2D measurements. It is shown that 2D-DIC can capture the material deformation with sufficient accuracy not only for planar specimens but also for certain scenarios involving out-of-plane motion (like balanced biaxial tension) by theoretical compensation of the strains.
Journal: SAE International Journal of Materials and
Manufacturing Citation: Agha, A., "Effectiveness of 2D
Digital Image Correlation in Capturing the Fracture Behavior of
Sheet Metal Alloys," SAE Int. J. Mater. Manf. 16(2):2023,
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One of the main technical challenges faced in the design and development of stamping dies and manufacturing is the complex springback response of sheet metal alloys. Springback is the elastic recovery in the material when unloaded after the forming operation. And the introduction of advanced materials like high-strength aluminum alloys and advanced high-strength steels (AHSS) exhibiting high strength and ductility makes it even more challenging. The magnitude of springback is directly proportional to the ratio of flow stress to Young's modulus of the material, which makes it typically high for such high-strength materials. Moreover, the anisotropic behavior of aluminum alloys and the multi-phase microstructures of AHSS result in strong tension-compression asymmetry leading to complex springback behavior.
In sheet metal forming and stamping operations, modeling the
behavior of sheet metal alloys for springback prediction is known
to be very challenging, not only because of the complex models
needed to account for kinematic hardening (such as the
Yoshida-Uemori Model) but more importantly because of the
experimental limitations of our ability to perform the complex
tests needed to calibrate such models. For instance, reliable
monotonic uniaxial compression tests and then cyclic
tension-followed-by-compression tests are essential for
characterizing the response of the material under those loading
conditions, providing quantitative evaluation of the Bauschinger
effect and tension-compression asymmetry in the material, and
ultimately generating the right data to calibrate the constitutive
This work tries to shed some light on this topic by introducing a new antibuckling device that is particularly designed to enable accurate and repeatable compression and cyclic testing. The device exerts side loading on the sheet test sample to prevent it from buckling during testing under compression loading conditions. The device is designed to address the limitations of other approaches and devices presented in the literature, and it features control and monitoring of side forces, self-centering, and the ability to achieve large plastic compressive strains. More importantly, digital image correlation (DIC) is integrated with the antibuckling device and testing load frame to provide accurate strain measurements.
In this study, DIC was used in a real-time mode (unlike the typical postdeformation mode) to facilitate accurate load reversal during cyclic testing. For validation, the presented setup was used for testing two selected materials with practical applications in the automotive body sector: AA6016-T4 and DP980 steel sheets. The results demonstrate how the developed setup and the integration with real-time DIC provide a robust and reliable means for generating high-quality curves for the different tests needed for the calibration of springback models.