Issue 39

O. Daghfas et alii, Frattura ed Integrità Strutturale, 39 (2017) 263-273; DOI: 10.3221/IGF-ESIS.39.24 269 The identified curves by Hollomon and Voce laws compared to the experimental hardening curves obtained in the two directions relative to the rolling direction (00° and 45°) are presented in Fig. 4a and Fig.4 b respectively. Then a comparison is made in order to show the most suitable law for the identification of hardening curves. A significant difference in result between the two laws is visible by zooming the curves. It is seen that in the homogeneous part of the plastic deformation the voce law describes the specimen fracture better than the Hollomon law for two loading directions from the rolling direction. By convention, the voce hardening law is selected subsequently to identify anisotropy behavior relating to this alloy. (a) ψ = 00° (b) ψ = 45° Figure 4 : Identification of the hardening curve: (a) ψ = 00° (b) ψ = 45°. Second identification step Using the simplex algorithm and using the non-quadratic Barlat criterion (2) and respecting the assumptions, the second step of identification strategy is equivalent to choosing the coefficients of anisotropy (c 1 , c 2 , c 3 , c 4 ) and the shape coefficient m (Tab. 5) while minimizing the squared difference between the theoretical and experimental results. c 1 c 2 c 3 c 4 m 0.3612 0.3431 0.113 1.0539 6.2486 Table 5 : Identification of anisotropic coefficients and a shape coefficient m.