Issue 19

G. Bolzon et alii, Frattura ed Integrità Strutturale, 19 (2012) 20-28; DOI: 10.3221/IGF-ESIS.19.02 24 aluminium foil and to the ultimate failure of the specimen. The appearance and evolution of the interfacial cracks are then clearly evidenced, for instance in the photographs 27 and 30 reported in Fig. 3. [mm] [mm] 10 20 30 40 50 60 0 10 20 -1 -0.5 0 [mm] [mm] 10 20 30 40 50 60 0 10 20 -0.2 -0.1 0 0.1 0.2 Figure 6 : The displacement field in the heterogeneous specimen under tensile test (loaded head on the left, fixed on the right), reconstructed by the correlation of the digital images 7 (the reference one) and 22 acquired during the test (see Fig. 3). DIC permits to follow the evolution of the displacement field all along the test in all locations of interest and to process this information for subsequent analyses. Opening and sliding relative displacements associated with the material separation process can be quantified by focusing attention on different material lines, for instance those sketched in Fig. 7. Results are represented in Figs. 8 and 9: the graphs in Fig. 8 show the evolution of the left (a) and of the right (b, c) boundary between the aluminium laminate and the paperboard composite during the tensile test, while the sequence of Fig. 9 evidence the relative displacements between the paperboard composite and the aluminium laminate, produced by removing the initial offset between the reference lines. This kind of information permits the identification of the fracture properties, inferred by the comparison with the result of the numerical simulation of the test. Figure 7 : Reference lines for the recovery of the relative displacements during material separation. S IMULATION OF THE LABORATORY TESTS he interpretation of the experimental results can be supported by the numerical simulation of the test, performed e.g. by the Finite Element (FE) model visualised in Fig. 1(b). Properly calibrated elastic − plastic constitutive models can interpret the response of the isotropic aluminium laminate and of the orthotropic paperboard composite, while the progressive fracture process can be simply simulated by non − linear spring elements, endowed with the piecewise linear traction − separation law schematized in Fig. 10(a), according to a cohesive − crack approach earlier exploited in different fracture mechanics contexts [12, 13]. In this investigation, classical von Mises plasticity model with exponential hardening and saturation strength is assumed to describe the continuum behaviour of the investigated aluminium laminate. The corresponding constitutive properties are deduced from independent laboratory tests: 3150 MPa equivalent elastic modulus; 5.45 MPa initial yield limit; 17.95 MPa ultimate strength; 34.5 hardening exponent. The considered cohesive law is characterized by five independent parameters (see Fig. 10a), which represent: the maximum force F max transmitted across the interface between the aluminium laminate and the paperboard composite at 0.5 mm separation distance, a value that accounts for the material deformability between the reference lines assumed on the paper and aluminium sides; the intermediate force F 1 that corresponds to the additional separation distance D 1 ; the residual force F plat carried by the polymer coating beyond further separation D 2 . T