Structural response of metal sheets under combined shear and tension
Introduction
Flat panels, made of metal sheets, are commonly used as an important structural element in defense, construction, automobile and space related industries. The performance of such structural panels depends on the mechanical behavior of their constituent materials and the relevant geometrical parameters. Hence, the mechanical characterization of metal sheets under in-plane shear or combined in-plane shear and tension is very important in understanding the structural behavior of such components under different loading conditions.
There are various specimen geometries and experimental techniques available in the literature for testing solid materials and metal sheets under pure shear loading conditions. Most of the experimental setups used for the planner shear evaluation of the specimen, consist of two rigid supports capable of providing in-plane parallel displacement to the different sections of the specimen. The Iosipescu shear test [1], [2] on a notched short beam specimen (Fig. 1a) is commonly used for characterizing the pure shear properties of isotropic and composite materials. Several other experimental procedures with various specimen shapes are also developed in the literature for testing thin metal sheets under in-plane shear. The simple shear test fixture (Fig. 1b) with a narrow specimen, fixed between rigid and movable holders on both sides [3], [4], [5], [6] and Miyauchi specimen (Fig. 1c) with two shear zones and three clamping areas [7], [8], [9] are also widely used for shear testing of metal sheets in a universal testing machine (UTM).
The V-notched rail shear method as per ASTM D 7078M-19 [10], [11] and the slotted shear test as per ASTM B 831-19 [12], [13] have also been used in the literature for testing of materials with commonly used UTM. The torsion testing of thin walled tubes [14], twin bridge shear test [15], in-plane torsion test of grooved specimens [16] are some of the other methods to determine the shear properties of metal sheets. The shear properties may also be determined using bi-axial testing machine [9]. Yin et al. [17] have compared the performances of three specimen types (Miyauchi type, ASTM B 831-19 and twin-bridge specimen) for the characterization of metal sheets. However, all the above referred experimental works (or procedures) are limited to testing of a narrow gauge length specimen under pure in-plane shear loading.
Similar to pure shear, the importance of understanding the behavior of structural materials under combined in-plane shear and tension is also addressed in the available literature. Bijlaard [18] proposed a rectangular specimen with diagonal groove (Fig. 1e). The unique geometry of the specimen allows it to obtain a combined state of shear and tensile stress. Hill [19], [20] provided asymmetric deep notches on the specimen (Fig. 1f), to create a favorable yield zone along the line connecting both the notch tips. Further modification to the Hill’s geometry was proposed by Hundy and Green [21] in 1954. The researchers introduced two sets of parallel anti-symmetric notches on the specimens (Fig. 1g) for testing copper, zinc and stainless steel, to obtain their plastic stress-strain relationship. Similar specimen geometry was also utilized by Lianis and Ford [22] in 1957, while evaluating the commercially pure aluminum. The authors also validated the Hill’s assumptions of stress uniformity across both the necking locations on the specimen. In-depth summary of the above articles is provided by Becque et al. [23]. In-addition, Becque et al. [23] used three different notched specimen geometries along with the DIC technique to evaluate the yield behaviour of the stainless steel. The study highlighted the importance of the notch geometry (Fig. 1h) to avoid the adverse end effects, and to ensure the stress and strain uniformity in the necking zone. In another related article, Jia et al. [24] have also proposed two different specimen shapes for understanding the interaction between shear and tensile stresses on the mechanical behavior of mild steel and high strength steel. Most of the above researchers have attempted to modify the specimen geometry in order to achieve a combined state of loading.
However in many research articles, in-addition to the geometry of the specimen, holding mechanism of the specimens are also designed in a manner to facilitate the mixed loading conditions. Arcan et al. [25] have proposed an experimental technique to test isotropic or composite plates (Fig. 1i) at different states of plane-stress (tension, in-plane shear and combined tension and shear). The narrowest cross-section of the butterfly shaped Arcan specimens is commonly considered as the reference area for evaluating the stress/strain of the material. However, there are few associated complexities with the wide Arcan specimen, such as strain homogeneity (elimination of stress concentration near the supports), the possibility of out-of-plane bending/twisting of the specimen under in-plane loading and loading mechanism. Voloshin and Arcan [26] have modified the size of the Arcan specimen to reduce the bending effects during the loading. Another important modification to the Arcan fixture was proposed by Yen et al. [27], by gripping of the specimen in the trapezoidal cutouts in between the two fixture plates. EI-Hajjar and Haj-Ali [28] have used large numbers of bolts (twelve) to hold the specimen between the plates. Greer et al. [29] have discussed the Arcan kinematics with reference to the different mounting configurations and highlighted the importance of avoiding the out-of-plane bending of the specimen (mode III loading component)
The Arcan fixture has been continuously used by several researchers. Tariq et al. [30] used butterfly shape specimens made of two different aerospace grade aluminum alloys and Arcan fixture to study the variation of material strength under shear loading to tensile loading. Daiyan et al. [31] reported an experimental study on the mechanical behaviour of polypropylene materials under in-plane shear stress using the Iosipescu and Arcan specimens. Taher et al. [32] have used a modified Arcan fixture for testing PVC foam, while Hung and Liechti [33] have studied the performance of Arcan specimen for fiber reinforced composites. Several researchers [34], [35], [36], [37], [38], [39], [40] have also used Arcan specimens for characterizing the fracture behavior of different materials under combined shear and tension.
Several theoretical studies on the elastic buckling of shear panels [41], [42] and plastic buckling of compressed plates [43], [44], [45] are available in the literature. However, studies on the plastic buckling behavior of thin specimens under combined shear and tension are scarce in the literature. The present manuscript is an attempt to understand the material and structural response of metal sheets under combined shear and tension using a combined experimental and numerical approach.
The structural behavior of moderately thick flat panels is a major concern for structural engineers. For example, the aluminum and mild steel shear panels [46], [47] are used to control the lateral displacement of buildings; the castellated web panels [48], [49] are used in long span beams. The large in-plane deformation behavior of such flat panels depends on the mechanical response of materials, while the possibility of plastic buckling additionally depends on the geometry of such structural panels.
Several experimental setups and specimen geometries are being used by the researchers for the determination of uni-axial (e.g., dogbone shape specimen), bi-axial (e.g., crucified specimen shape) and shear (e.g., Iosipescu shear test, Arcan fixture) response of the material during its elastic and plastic deformations. However, the authors have observed severe out-of-plane deformation of thin (1.0 mm, 1.5 mm) metallic butterfly shaped specimens during the in-plane shear test in Arcan fixture. In an attempt to achieve the ultimate shear strength of metallic plates and the corresponding in-plane plastic deformation, the authors have exhaustively explored the possibility of using comparatively thicker specimen and modified specimen geometry, to reduce the level of out-of-plane deformation (correspond load eccentricity) during the in-plane shear experiment.
Four different geometries of the specimens are judiciously selected (designed), so that some of the specimens undergo large in-plane strain without significant out-of-plane deformation, while the other specimens buckle during the in-plane plastic deformation. In the absence of plastic buckling, the constitutive relations of aluminum (Al1100) and mild steel (IS 1570) plates under pure tension and pure shear are obtained. The corresponding material properties may subsequently be used to simulate the elastic / plastic buckling loads of other sets of specimen shapes and the flexural behavior of different flat panels.
Section snippets
Experimental procedure
The materials and different geometries of the Arcan specimens are documented in this section along with the fixture details, loading system and measurement technique. The aluminum (AL 1100) and mild steel (IS 1570) sheets of 2 mm thickness are commercially procured from a Delhi based supplier. The chemical composition of the materials are obtained from the spectrochemical analysis and presented in Table 1.
Numerical simulations
An effort is also made to simulate the mechanical response of all the four specimens under different loading conditions using FEM. For this purpose, all specimens are modeled here using the 8-noded linear brick element (C3D8R) in ABAQUS/Explicit. In order to avoid the hourglass effect ABAQUS provides the artificial stiffness to this element [53], [54]. Thus C3D8R has only three degrees (translational) of freedom per node. This linearly reduced integration element is considered to be
Results and discussions
The performance of the four different shapes of Arcan specimens under pure shear and mixed mode (I/II) loading is investigated through an exhaustive experimental and numerical study. This section reports the observations from 32 experiments (four specimen shapes for each of Al-1100 and IS-1570 are tested at 0°, 30°, 60° and 90° loading angles) repeated nine times (three experiments at 1 mm/min, 2 mm/min, 3 mm/min deformation rates). Hence, a total of 286 (32 × 9) number of experiments are
Conclusions
The mechanical response of four specimen geometries is examined here under in-plane shear and mix mode (I/II) loading conditions. The modified Arcan fixture is used for loading the specimens at different orientations and the 3D digital image correlation technique is used to estimate the full field displacement and strain profiles. The responses of the specimens are also simulated using commercially available finite element software ABAQUS. Results are reported for 2 mm thick aluminum (AL-1100)
Data availability
All the experimental data, generated during this study are compiled and presented in the submitted article.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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