PSI - Issue 57

Amira Aboussalih et al. / Procedia Structural Integrity 57 (2024) 848–858 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

849 2

Nomenclature 11 , : Uniaxial Strains. : total deformation : élastic deformation : plastic deformation ε max ,ε min ∶ extreme values of the axial strain γ θz : angular deformation γ max , γ min ∶ extreme values of angular deformation : initial size of the elastic domain : axial stress : torsional stress σ moy : mean stress  ( p ) Function expresses the cyclic hardening of the material .

p: cumulative plastic deformation X : kinematic hardening tensor b : Constant indicating the speed of stabilization R : isotropic work hardening variable.

Q : hardening memory C : kinematic constant N ∶ cycle number 2 : second invariant of the tensor E : Young’s modulus of elasticity

.

f : charging function : deviatoric part of the Cauchy stress tensor

2. Methodologie The field of pure reversibility is delimited in the space of the stresses by a surface of load described by von Mises from which the plastic flow can occur [19-20]. This surface is represented in the constraint space by a load function of the following form : ( ) yi f J X R   = − − − (1) The material studied is characterized by its resistance to rupture and its ability to work hard.Consequently the work hardening is manifested by the expansion of the load surface corresponds to an isotropic work hardening (R) and the displacement of its center corresponds to a kinematic work hardening (X) . The evolution of R is given by: (2) With: Q and b constants of the material which have the effect of introducing a progressive hardening or softening. The evolution of kinematic hardening (X) is given by: ( ) ( ) p Xdp dX C p d p   − = ( ) d R b Q R d p = −

3 2

(3)

, dp is the increment of the cumulated plastic deformation 1/ 2 : = p p d d dp  

3 2

  

  

(4)