Issue 53

R. Harbaoui et alii, Frattura ed Integrità Strutturale, 53 (2020) 295-305; DOI: 10.3221/IGF-ESIS.53.23 297 where D  is the deviator of the stress tensor of Cauchy (incompressible plasticity). The hardening function σ s ( α ) plays the role of the thermodynamic function associated with the internal variable α  c ( D  ) : equivalent stress of the plasticity criterion. Function   D c   satisfies the following condition if a > 0 :     D D c c a a      (2) The evolution of the surface load is represented in the spatial deviators of constraints, which are defined as follows: D D D 1 2 3 = σ ; = σ sin θ cos2 ψ ; = σ sin θ sin2 ψ x cos x x  (3) Using the special configuration of space deflectors, the general form of the equivalent plane stress is written as follows:       D D c c 1 2 3 σ = σ , , = / f θ ,2 ψ x x x   (4) Any type of criterion can be written in the following form:   D s f( θ ,2 ψ )= / σ α  (5) The angle  which defines the orientation of  D is presented in Table2 and ψ the off-axis angle. Test Expansions Equibiaxes (E.E) Simple Traction (S.T) Large Traction (L.T) Simple Shear (S.S) θ 0 π /3 π /6 π /2 Table 2: The angle θ respective to four tests [9-10]. First, to identify the hardening curve it is necessary to choose an appropriate analytical law. Second, an identification of the parameters that define the material anisotropy is also required. For this step, the CPB06 criterion [19-23] is chosen to identify the behavior of AZ31B-H24 magnesium alloy. The equivalent stress of CPB06 criterion is defined as follows:   1/ 3 1 σ m m c i i i q kq           (6) where q 1 , q 2 and q 3 are the eigenvalues of the tensor q q = C : σ D (7) q : modified stress deviator tensor qi: the principal values of the tensor q. m: the degree of homogeneity also called form coefficient. σ D : deviatoric stress tensor (incompressible plasticity) C : 4th order tensor of the linear transformation. The components Cij are represented by (Voigt notation):