Issue 49

C. Bellini et alii, Frattura ed Integrità Strutturale, 49 (2019) 791-799; DOI: 10.3221/IGF-ESIS.49.70 793 Both Marciniak and Nakajima tests can be used for FLC experimental determination [17]; Banabic's work [18] examines different methods for determining the FLC. The simplest experimental method for calculating the FLC of a sheet is the Nakazima test. This test consists in the movement, at constant speed, of a hemispherical punch against the sheet metal clamped between the die and the blank holder. The sheet is thus subjected to stretching up to the onset of the necking or fracture. To induce different deformation states in the material, the test is carried out on rectangular specimens with different width-length ratio. To detect strains on the sheet metal, a reference grid is drawn on the samples before performing the test. In this work, adopting the FEM code and the experimental results presented in [19], the friction influence on the formability of the AA6060 aluminium alloy is highlighted. The friction effects on sheet formability are very important [20]; in fact, Yan et al. presented a scale factor to adjust the Wanheim/Bay friction model [21], Ma et al. studied the effect of temperature on the tribological behaviour in tube forming [22], Wang et al. investigated the substitution of zinc phosphate precoat with another lubricant coating [23], Hol et al. introduced a physical based model for friction simulation in full- scale modelling, taking into consideration the surface topography variation [24], Wang et al. examined the dry forming process carried out by means of a coated tool [25], Hol et al. presented an advanced friction model, based on Coulomb law, suitable for large-scale forming modelling [26], Zhang et al. studied the effect of reciprocal speed and surface roughness on the Coulomb friction coefficient through FEM simulations [27] and Wang et al. performed a study on the challenges and trends of friction analysis in sheet metal forming [28]. E XPERIMENTAL ACTIVITY he material considered in this study is the aluminium-magnesium-silicon alloy named AA 6060. It is characterized by the following chemical composition by weight: Al - 0.6% Si-0.3% Fe-0.1% Mn-0.6% Mg-0.1% Cu-0.15 % Zn- 0:05% Cr-0.1% Ti. The constitutive law of the material was determined by the tensile test according to the European standard UNI EN 10002-1. The results of the tensile test, carried out on 1 mm thick specimens, are reported in [19]. The material is thus characterized in the plastic field by a constitutive equation that can be expressed by the power law: n K    (5) where ε and σ are the equivalent strain and the equivalent stress, respectively; while K is the strength coefficient and n is the hardening index of the material. The experimental activity involves the execution of a stamping operation performed on square-shaped specimens clamped between the die and the blank holder, both presenting a circumferential shape with a radius of approximately 83 mm, and subjected to the action of a hemispherical punch with a radius of 60 mm. The tests are conducted using the equipment designed at the DICeM Laboratory of the University of Cassino. This apparatus is equipped with a load cell that allows detecting the force-stroke curve of the punch. Further details on the experimental equipment are reported in [19, 29]. The tests are conducted both in the absence and in the presence of lubrication, in the latter case by using a polytetrafluoroethylene sheet (PTFE) as a lubricant between the punch and the sheet. The influence of friction on the results of the Erichsen test conducted on sheets made of different aluminium alloys and on DC05 steel was studied by the authors in [29, 30]. In order to determine the principal strain in the fracture conditions of the material, a grid of circles with a diameter of about 3 mm is drawn on the specimens before executing the forming test. The sheets are cut according to the scheme shown in Fig. 2. N UMERICAL ACTIVITY he stamping test is simulated by FEM model using the commercial calculation code MSC.Marc 2005. It consists of a trial similar to the Nakazima test considering only the geometry shown in Fig. 2. In [19] it is shown that the results of the numerical simulation conducted by means of a two-dimensional analysis (which uses axisymmetric elements) are identical to those achieved through a three-dimensional analysis, that requires shell elements, that are heavier than the axisymmetric ones. Therefore, all the results cited below refer to the lighter two-dimensional analysis. Fig. 3a shows the layout of the equipment used as well as the sheet discretized with axisymmetric finite elements. T