Abstract In this paper the formability of AA2024-T3 metal sheets is experimentally analyzed. For this purpose, a series of Stretch-Bending and Incremental Sheet Forming (ISF) tests are carried out. The former tests allow determine the formability limits through the evaluation of necking and fracture using the optical deformation measurement system ARAMIS® and measuring the thickness strains along the fracture line. The latter are performed with the aim of confirming the validity of these limits. In this case, the spifability, formability in Single Point Incremental Forming (SPIF), was studied in the light of circle grid analysis by means of the 3D deformation digital measurement system ARGUS®. Different punch diameters are used in both processes. The results exhibit the importance of the accuracy in the setting of the formability limits as well as the variability that these limits present depending on the forming process or some variables such as the tool radius. © 2013 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of Universidad de Zaragoza, Dpto Ing Diseño y Fabricación. Keywords: Formability limits; Stretch-Bending; Incremental Sheet Forming (ISF); Single Point Incremental Forming (SPIF). © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license.Selection and peer-review under responsibility of Universidad de Zaragoza, Dpto Ing Diseño y Fabricacion  34152
1. Introduction The AA2024-T3 is a thermally treated Aluminium Alloy widely used in the manufacture of aircraft structures, especially wing and fuselage skins under tension. So, in order to avoid production problems and to optimize the forming processes it is essential to establish accurate formability limits. In this sense, the Forming Limit Diagram (FLD) is the most useful tool for evaluating the workability of sheet metals. They show, in the principal strain space, the combinations of strains at the onset of local necking, FLD at necking or FLC (forming limit curve), and at the beginning of ductile fracture, FLD at fracture or FFL (forming fracture line). High ductility materials usually start the failure process with the onset of strain localization along a narrow stripe, leading to the formation of a neck (necking). The material deforms continuously within this neck, following approximately a near plane strain state, until the ductile fracture takes place. On the contrary, for low ductility materials the fracture may occurs in absence of the necking process, being the formability of the sheet controlled by ductile fracture mechanisms. The Fig. 1 depicts the formability limits, by means of the FLD at necking and fracture, for high-ductility and for low-ductility materials, which is in fact expected in the case of the AA2024-T3 1.2 mm thickness metal sheets, considering previous experimental results such as Vallellano et al. (2008) and Centeno et al (2012a).     Fig. 1. FLD at necking and at fracture for high-ductility (left) low-ductility (right) materials. The occurrence of fracture in absence of necking is more likely to occur in stretching operations, especially within near equi-biaxial conditions, where the sheet undergoes a biaxial strain state (see Fig. 1), and in incremental forming operations under certain forming conditions characterised by small punch diameters and step downs. Such facts add an extra complexity to the analysis of failure. In addition, recent studies show that the local evolution of the stress/strain gradient through the sheet thickness is essential to explain the bending effect in formability, focusing mainly on the strains of both the inner and the outer surfaces at the process zone of the metal sheet. In fact,
depending on the severity of the strain gradient, two types of failures can be expected: (1) a Necking-Controlled Failure, which takes place when the entire sheet thickness becomes plastically unstable; and (2) a Fracture-Controlled Failure, which arises when the outer surface of the sheet fracture. In this way, in ISF processes failure changes from type (1) to (2) as the radius of the forming tool decreases. In fact, some recent studies allow conclude that the failure mode above described clearly depends on the parameter t0/R, ratio of the initial sheet thickness t0 to the radius of the forming tool R, as pointed out for instance by Stoughton and Yoon (2011), and Vallellano et al. (2010) in stretch-bending, and by Silva et al. (2011) in the case of SPIF. In this sense, the authors also suggested in Centeno et al. (2012b) the importance of quantifying the enhancement of formability in ISF due to the bending effect by means of this t0/R ratio. In this paper the feasibility of fracture limits for AA2024-T3 metal sheets is discussed. For this purpose, a series of stretch-bending and Single Point Incremental Forming (SPIF) tests are carried out. The stretching and stretch-bending tests permitted to determine the conventional formability limits through the evaluation of necking and fracture. The SPIF tests were performed with the aim of confirming the verisimilitude of these limits. The results exhibit the importance of the accuracy in the setting of the formability limits as well as the variability that these limits present depending on the forming process or some variables such as the tool radius. 2. Experimentation In order to obtain and discuss the formability limits of the AA2024-T3 sheets, a series of stretch-bending and single point incremental forming tests have been carried out. The methodology followed to obtain the formability limits for each case is exposed in this section. 2.1. Stretching and stretch-bending tests A series of Nakazima tests (hemispherical punch of Ø100 mm) have been carried out using three different specimen geometries with the aim of obtaining the conventional forming limits, represented by the FLC and the FFL as discussed above. The Nakazima tests were performed in a universal sheet metal testing machine Erichsen 142-20 (see Fig. 2), being the testing conditions taken according to the ISO standard 12004-2 (2008). The punch velocity was set to 1 mm/s and the lubricant at the interface punch-sheet was Vaseline + PTFE + Vaseline.     Fig. 2. Universal sheet metal testing machine (left) and a scheme of the experimental setup (right). The optical deformation measurement system ARAMIS®, based on digital image correlation technique, was utilized to evaluate along the tests the strain distributions at the outer surface of the sheets by following the methodology explained in Martínez-Donaire et al. (2008). For the whole Nakazima testing plan, the material presented a fracture-controlled failure, i.e. all the metal sheets failed directly by fracture in absence of a distinctive necking. Considering this behavior, two failure curves were set: (1) the Engineering Fracture Line (EFL) and (2) the Fracture Forming Line (FFL). The EFL was obtained by measuring the characteristic major and minor strains around the failure zone at the last image recorded by ARAMIS® just before the crack appearance (see Fig. 3). In the present case, the EFL would almost coincide with the FLC at necking calculated by using the ISO standard 12004-2 (2008) for this material. This can be explained by the small calculating window around the fracture line corresponding to the behavior of this material (for more details see Martínez-Donaire et al., 2010).Fig. 3. Contour of major (left) and minor strains (right) at last image before the crack appearancein a Nakazima test near plane strain conditions.On the other hand, the Fracture Forming Line (FFL), which for this low-ductility material does not appear as astraight line, was evaluated by following the  principles explained in Silva et al. (2011). The procedure for constructing the FFL starts by measuring the thickness at fracture at several places along the crack in order toobtain the average thickness strain, as shown in Fig. 4 (left). Average thickness strain was evaluated at both sidesof the crack for every tested metal sheet. In addition, some tested sheets were cut and the thickness was measuredfrom a profile view, as shown in Fig. 4 (right), in order to validate the previous thickness measurements along the crack. The average minor strain was evaluated along the fracture line at the last image recorded by ARAMIS® justbefore the crack appearance. Finally, major strain was calculated by volume constancy:(1)Finally, the application of the same methodology for evaluating fracture to previous stretch-bending tests(whose results can be found in Centeno et al., 2012b), AA2024-T3可成形性金属板英文文献和中文翻译:http://www.751com.cn/fanyi/lunwen_31593.html