Abstract
The in-plane tensile-compressive test is a key method for studying plastic behavior under complex loading. This study presents a novel anti-buckling fixture designed for cyclic testing. The device can conduct monotonic tensile-compressive tests with deformations of up to 10%. The specimen is encased in an acrylic block for structural stability and to prevent buckling. Its application and impact on the force-displacement curve have been addressed. The AutoGrid optical strain measurement system was integrated with the fixture for strain analysis, and its accuracy was systematically evaluated. The developed fixture is well-suited for accurately describing the plastic behavior of materials under complex loading paths and it aids in precisely determining the kinematic hardening characteristics.
1 Introduction
Understanding Bauschinger behavior is crucial for accurately simulating and predicting the formability of sheet metal. Springback, for example, is an important measure of formability and poses a considerable issue in the cold forming of sheet metal [1]. Therefore, effective Finite Element Method (FEM) analysis to predict springback requires consideration of the cyclic hardening characteristics of materials [2–4].
Uniaxial in-plane tensile-compressive tests are the common methods to investigate the Bauschinger behavior of sheet metals. Due to non-uniform strain distribution, in-plane shear tests and bending-reverse bending tests are challenged [5, 6]. The uniaxial in-plane tensile-compressive test provides uniform deformation within the measured area [7]. However, a significant challenge arises from the tendency of sheet materials to buckle under high levels of compressive strain, severely restricting the range of compressive strain that can be applied [8]. Consequently, studying the cyclic loading behavior in metal sheets becomes significantly more complex.
Numerous methods have been extensively researched in the literature for measuring large-strain cyclic plastic deformation. Yoshida et al. [9] investigated the behavior of bonded mild and high-strength steel specimens under cyclic loading. The steel specimens were subjected to a maximum cyclic strain of approximately 8%, a significantly high level for such tests. To address the concern of buckling, this study utilized a specialized device called a specimen holder, which was equipped with coil springs. During the test, strain measurements were obtained using an extensometer directly attached to the specimen. Friction at the interfaces between the bonded specimen and any supporting apparatus was challenged. Importantly, the study demonstrated that the effect of pressure on the stress-strain behavior was insignificant. However, high pressure applied to the specimen in certain testing situations can change the material stress-strain behavior. Boger et al. [7] focused on improving the performance of compression tests for thin sheet materials by using a laminated specimen system. To carry out these tests, the study employed a specialized apparatus that helped to support the thin sheet material during the compression loading cycle. The apparatus prevented these issues by stabilizing the specimen as it was compressed. However, the researchers encountered a significant challenge like friction forces added extra resistance to the compression. Stoudt et al. [10] carried out research that closely parallels the work of Boger et al. [7] focusing on the mechanical properties of steel. Their study successfully generated the compressive curve corresponding to a pre-strain of 4%. Kuwabara et al. [11] expanded the limited strain range by incorporating two pairs of comb-shaped supports. Male and female die enhanced this design to slide one another as the sample is compressed. However, the device has some limitations. The specimen's long and narrow design makes it challenging to maintain good axial alignment. This mismatch decreases the possible compressive strain range before buckling. M Härtel et al. [12] improved on the technology demonstrated by Kuwabara et al. [11]. The configuration comprises clamps to secure the sample and four adjustable, comb-shaped elements designed to restrict out-of-plane deformation. Strain measurements are captured using a Digital Image Correlation (DIC) system. Friction between the clamps and the specimen was still an issue. Cao et al. [5] introduced a novel approach as a double-wedge setup that applied lateral force. The double-wedge mechanism was designed to counteract buckling by exerting force from the sides of the specimen. However, the lateral force in this setup was generated using six screws, which posed a significant challenge. In addition, to accurately monitor strain, two fins were added to each test specimen, offering a clear surface for the laser to track. These fins were essential for the use of an expensive laser extensometer, a precise tool that measures strain by detecting small displacements. Chang et al. [13] developed an innovative in-plane tensile-compressive device. The clamping segment consists of an upper and lower fixture. The upper fixture is attached to the force sensor of the testing machine and serves to secure the top end of the specimen. Sharp teeth firmly grip both ends of the specimen on the inner surfaces of the fixtures. The study applied two T-shaped solid plates, with fixed and movable ends, to provide normal support to the specimen during continuous tensile-compressive testing. The fixed end is connected to the respective upper or lower fixture, while the movable ends are guided in a straight reciprocating motion within a groove. However, some surfaces of the specimen remain unsupported during the sliding movement and therefore, the study was not fully free from buckling. To enhance the design, a special cutting edge was introduced to apply the extensometer. This new edge was narrower than the specimen thickness and was challenging to apply.
Almost all present fixtures have their challenges, as all systems utilize an extensometer to gauge the strain. Therefore, it necessitates the incorporation of specialized fins along the specimen sides and requires properly quantified pressure and friction forces. Its application is complicated. In addition, several significant problems existed such as their inability to accommodate large strains or to effectively manage the potential for buckling under compressive loads. Consequently, it becomes essential to develop a new tensile-compressive device that is capable of continuous testing. The present work aims to bridge the gaps identified in previous studies and to contribute to the advancement of tensile-compressive testing methodologies.
The challenge related to strain measurement can be mitigated by substituting conventional strain measurement techniques with the DIC method. The digital image correlation method has demonstrated efficacy in measuring two-dimensional strain across various applications [14–17]. DIC [18–20] is a powerful optical technique widely utilized in the field of experimental mechanics for comprehensive displacement and strain measurements across an entire surface. The quantitative DIC approach was effective and was validated through extensometer recordings to further confirm the suitability of full-field optical methodology for fatigue monitoring [21]. Cruz et al. [22], confirmed the possibility of using DIC for tension-compression tests.
In this study, Vialux AutoGrid optical strain measurement method was configured with the new anti-buckling fixture. The AutoGrid measuring system applies four Charged-Coupled Device (CCD) cameras with mobile measuring heads, to track the deformation of the grid created on the surface of the specimen with a special printing technique before the test. The cameras are pre-calibrated and are able to measure the grid distortion with high precision. From the measurement of extended or distorted grid points, three-dimensional (3D) strains can be calculated by an automatic evaluation method supported by the program provided with the system [23]. The Vialux AutoGrid optical strain measurement system would be fully integrated with the universal tensile machine and record the strain distribution on the surface of the specimen. To validate the applicability of the method, a tension-unloading test on aluminum alloy AA6082-T6 was conducted without the anti-buckling fixture. The experiment involved the simultaneous use of a conventional extensometer and the Vialux AutoGrid optical strain measurement system. It is essential to look into the decline of the apparent elastic modulus to correctly forecast the kinematic hardening behavior of the material.
2 Constitutive modeling of cyclic plastic deformation in AutoForm
The stress-strain curve of sheet metal under loading and reverse loading is depicted in Fig. 1 [4, 9]. When it comes to reverse loading, specific hardening behaviors can be identified and grouped into four primary components: the Bauschinger effect, transient behavior, work hardening stagnation, and permanent softening. Together, these phenomena are collectively referred to as the Bauschinger behavior of the material.
Schematic tensile-compressive curve of sheet metal with reversal stress and strain
Citation: Pollack Periodica 2025; 10.1556/606.2024.01252
Given the intricacy of the loading-unloading-reverse loading cycle, numerous researchers have proposed advanced constitutive models to more effectively capture the Bauschinger effect. Wagoner et al. [24] observed that classical elastic-plastic constitutive models continue to be extensively utilized in springback simulations due to their computational efficiency. A combined hardening model, incorporating both isotropic and kinematic hardening, provides a more accurate solution for reverse-loading scenarios [25–27]. Yoshida et al. [28] introduced the kinematic hardening model, which accurately describes both the Bauschinger effect and work-hardening stagnation. Furthermore, E. Lee et al. [29] developed a kinematic hardening model that simultaneously captures the Bauschinger effect and anisotropic hardening responses. This model was validated through experiments, proving to be a versatile model for both monotonic and cyclic loading conditions.
In order to model the work-hardening stagnation, the accumulated equivalent plastic strain
3 Design and development of a new anti-buckling fixture
The new experimental anti-buckling fixture was developed by modifying the existing design at the Institute of Materials Science and Materials Technology at the University of Miskolc to solve the difficulties of the existing fixture. These modifications were aimed at improving the functionality and performance of the fixture for more precise and reliable testing. The key focus of the alterations was the clamp section. The supporting mechanism of the existing fixture uses an extensometer for strain measurement and utilizes two rows of 0.5 mm thick high-strength steel plates, precisely positioned 1.5 mm apart. These steel plates maintained proper alignment and secure positioning of the specimen during the experiment and it is compatible with an extensometer [33]. However, as the distance between the support plates increased during tension, an unintended consequence emerged, the unsupported length of the specimen expanded. This elongation in the unsupported length resulted in gaps where the specimen lacked adequate support, giving rise to several challenges. A significant issue stemming from this scenario was the non-uniform distribution of stress across the specimen's surface. By replacing the original clamp section with an improved version, the modifications ensured better stability and alignment of the test samples.
Due to the aforementioned factors, the steel plate supports of the existing anti-buckling fixture were replaced with wedge-shaped acrylic blocks. This idea draws inspiration from the wedge apparatus designed by Cao et al. [5]. This transition facilitated the shift from the traditional strain measurement method to optical strain measurement. Acrylic blocks were selected for their exceptional optical clarity [34, 35]. Therefore, the fixture was integrated with the optical strain measurement system for comprehensive full-field strain measurements.
A new anti-buckling fixture has been specifically designed for monotonic tension-compression testing of sheet metal. The fixture consists of several components and its design incorporates four wedge-shaped acrylic blocks as it is shown in Fig. 2, which serves a dual purpose. They stabilize the specimen and enable the control and recording of slide forces through spring coils. These coils are crucial for maintaining uniform force distribution and effectively managing any lateral movements. Four same-thickness wedge-shaped blocks are used for proper contact and position with each other and alignment. The front and rear acrylic block holders have been specifically designed to guarantee accurate alignment of the gauge surfaces of the specimen with the four acrylic blocks. This design ensures a secure and uniform fit around the surface of the specimen, providing precise and reliable measurements. To ensure that the blocks maintain the necessary contact pressure with the specimen, a pair of pre-load screws was specifically created. These screws are responsible for regulating the normal force on both the front and rear acrylic block holders. In addition to the pre-load screws, four leveling screw pins have been used to accurately level the fixture with the specimen. Therefore, these leveling screw pins minimize the risk of misalignment, slippage, and twisting of the specimen during the test. This ensures the integrity of the testing process.
The new anti-buckling fixture, a) assembled, b) disassembled (1-specimen; 2-front acrylic block holder; 3-pre-load screw; 4-acrylic blocks; 5-rear acrylic block holder; 6-leveling screw pins; 7-coil spring holder; 8-coil spring)
Citation: Pollack Periodica 2025; 10.1556/606.2024.01252
Teflon sheets were added at the contact points between the wedge-shaped acrylic blocks, the specimen, and the specimen holder. It helps to decrease friction, allowing for smoother movement and reduces wear during repeated experiments. Figure 3 demonstrates the monotonic tension-compression procedure of the fixture on the tensile testing machine. Figure 3a depicts the fixture's initial position. To ensure the structural stability of the specimen and prevent buckling during cyclic testing, it is essential to fully encapsulate it within the acrylic block. As it is depicted in Fig. 3b, the testing apparatus should commence from a pre-compressed state. However, it is imperative to recognize that this pre-compression may introduce variations in the test results. Even though the normal pressure exerted by the pre-load screws could be controlled by four leveling screw pins, a little variation may affect the contact friction between the acrylic block and specimen and is a significant variable that can substantially influence the experimental outcomes because. Therefore, it is crucial to consider those factors when calibrating the applied force to guarantee the reliability and reproducibility of the test data. The position after applying tension and compression load using the tensile testing machine is shown in Fig. 3c and d.
The testing procedure of the fixture, a) initial position of the fixture, b) pre-compression of acrylic blocks by a displacement
Citation: Pollack Periodica 2025; 10.1556/606.2024.01252
4 Results and discussion
The effects of the stored force generated by pre-compressed acrylic block wedges, variations in the normal pressure applied by the preload screws, and any uncontrolled factors during the tests are depicted in Fig. 4. To investigate these effects, the study conducted six repeated full-cycle upsetting tests using a newly developed device, with a rectangular specimen positioned within the gauging area of the fixture. In this configuration, the specimen remained undeformed, enabling an evaluation of the device's impact. Figure 4a displays the time-displacement (disp.) curve across different regions of the test. Figure 4b illustrates the maximum, minimum, and average effects of the fixture on the force-displacement curve, incorporating all six measurements taken at various stages of the cycle. While the device's influence appears minimal in the tensile and re-tensile regions, it shows a significant effect in the unloading and compression areas.
The device affects a) the time-displacement profile of the test setup, b) the effect of the device on the displacement-force curve (line AB-tensile region; line BC in Fig. a and line B'C in Fig. b - unloading region; line CD-compression region; line DA in Fig. a and line D'A in Fig. b - re-tensile region)
Citation: Pollack Periodica 2025; 10.1556/606.2024.01252
Consequently, the force derived from Eq. (3a) will be added to the measured values in the tension and re-tension region. In contrast, the force obtained from Eq. (3b) will be added to the measured values in the unloading and compression region. This approach allows for a comprehensive analysis of the impacts of the new anti-buckling fixture on the material deformation behavior.
Figure 5a presents the force-displacement curve for the full cycle monotonic tension-compression test of W-tempered 6,082 aluminum alloy at 2% deformation using the new anti-buckling before and after the device effect compensation. The monotonic tension-compression test at different percentage deformation for positive displacement is shown in Fig. 5b. Those regions are important for the parameters related to the kinematic hardening behavior of the material in AutoForm commercial FEM code.
Monotonic tension-compression test for W-tempered 6,082 aluminum alloy using a new fixture, a) before and after compensation of the device effect, b) at different amounts of deformation after compensation of the device effect
Citation: Pollack Periodica 2025; 10.1556/606.2024.01252
In optical strain measurement, 2 × 2 mm square grids were painted to the surface of the specimen. A length of 24 mm, measured between 13 points at the center of the gauge surface, was chosen as the initial measurement length. However, a conventional measurement was performed using a 25 mm gauge length clip-on extensometer, aligned with the longitudinal axis of the specimen to record elongation. Time-change in displacement (ΔL) and stress-strain diagram for AA6082-T6 aluminum alloy were used to evaluate both ways of strain measurement as it is shown in Fig. 6. As it can be seen in Fig. 6a, the investigation revealed a notable discrepancy of 5% in the measurement of displacement change when comparing conventional strain measurement techniques to optical strain measures. This variation happened due to the changes in the initial length of the test. However, any alteration cannot lead to significant differences in the strain measurement. Finally, the above results insights both methods of strain measurement give the similar results and show good agreement.
a) Time-change in displacement curve, b) stress-strain curve
Citation: Pollack Periodica 2025; 10.1556/606.2024.01252
To ensure the compatibility of the AutoGrid optical strain measurement system with the new anti-buckling fixture, the monotonic tension-compression test of W-temper 6,082 aluminum alloy at 10% deformation was converted to a stress-strain diagram. The experiment was performed using a universal material testing machine setup equipped with a new anti-buckling fixture, as it is illustrated in Fig. 7. These findings are significant because they enable a more in-depth analysis of the Bauschinger effect. The important regions of the kinematic hardening behavior of the material can be clearly seen in Fig. 8. A deeper understanding of these regions will significantly enhance future research efforts, as it will allow for a more precise examination of the material response under cyclic tests.
Experimental setup (1-anti-buckling fixture, 2-CCD camera, 3-grid point detection in ViaLux code)
Citation: Pollack Periodica 2025; 10.1556/606.2024.01252
Single cyclic tension-compression of W-temper 6,082 at 10% deformation
Citation: Pollack Periodica 2025; 10.1556/606.2024.01252
5 Conclusions
A unique anti-buckling fixture was developed to facilitate in-plane tensile-compressive tests, allowing for a detailed examination of plastic deformation in sheet metal. This fixture has been specifically designed to support monotonic tensile-compressive tests, achieving up to 10% deformation, and is compatible with standard universal testing machines. Additionally, effective methods have been outlined to compensate for and mitigate the impact of clamping and friction-related forces, which are critical in maintaining the accuracy and reliability of the measurements during testing.
The AutoGrid optical strain measurement method was set up in conjunction with the anti-buckling fixture to facilitate accurate strain measurement. This configuration enables precise monitoring of strain distribution during testing. A uniaxial tension-unloading test was conducted simultaneously to verify the accuracy of the optical strain measurement system. The investigation shows that the AutoGrid optical strain measurement system is a reliable non-contact optical measurement method for strain analysis. Therefore, DIC offers precise and trustworthy strain measurements for in-plane tensile-compressive tests, making it a competitive substitute for conventional extensometers, particularly in situations where contact-based measurements are difficult to perform. This development has great potential to improve our comprehension and forecast of material behavior in sheet metal forming operations.
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