Issue 38

A. Znaidi et alii, Frattura ed Integrità Strutturale, 38 (2016) 135-140; DOI: 10.3221/IGF-ESIS.38.18 138  Validation strategy In the particular case of Magnesium sheets where anisotropy is present, the identification of this constitutive law requires the identification of the hardening function, the anisotropy coefficients, the form factor m and r (  ) the Lankford coefficient. Using as a hardening function a Hollomon law: n s k    (8) And as a plasticity criterion using the Barlat model [6]: m m m m c q q q q q q 1 2 2 3 1 3        (9) Where q 1 , q 2 and q 3 are the eigenvalues of the tensor q c s a i i (q) - ( ) 0. Where (a ) : thus (a ) :        q A q A σ (10) Using the simplex algorithm and using the plastic Barlat model and respecting the assumptions, the identification of the thin Magnesium sheet is equivalent to choosing the model coefficients while minimizing the squared difference between the theoretical and experimental results. ψ k n 00° 408.5 0.102 22.5° 410.6 0.096 45° 425.6 0.101 67.5° 432.5 0.0901 90° 437.1 0.0873 Table 2 : Identification of the constants of hardening law for different tractions tests. Knowing that the coefficient n is the same for all tests as demonstrated at the beginning of this work, by convention we choose n for traction in direction ψ = 00° as reference. For n =0.102, we present different values of k (see Tab. 3). ψ k 00° 418.1 22.5° 418.1 45° 427.1 67.5° 447.3 90° 455 Table 3 : Identification of the constant hardening law for fixed n. In Fig.1, the experimental hardening curve (exp) and the curve identified from a model (iden) using an average value of n are represented. For tensile tests, the models (iden) give a clear fit between the theoretical and experimental results. Our second identification step amounts to determining the coefficients of anisotropy ( f, g, h, n’ ) and the shape coefficient m (Tab. 4), considering the non-quadratic Barlat's criterion (9).