Issue 53

R. Harbaoui et alii, Frattura ed Integrità Strutturale, 53 (2020) 295-305; DOI: 10.3221/IGF-ESIS.53.23 298 C= 11 12 13 12 22 23 13 23 33 44 55 66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C C C C C C C C C C C C                     The parameter k may be determined from experimental values of σ tr and σ cp :           1 1 1 2 2 , 2 2 1 m m m tr cp tr cp tr cp m m tr cp tr cp h k h h                           (8) k: the parameter of the material, the ratio between the uniaxial yield in traction σ tr and the uniaxial yield in compression σ cp allowing the description of the differential effect of resistance h: is a variable that defines the history of the material To ensure the convexity of the plasticity surface, we fix m ≥ 1, -1 ≤ k ≤ 1 The hardening functions   p s     used are: Hollomon law [24] ( Hol ψ °):     n p p s K     ) (9) Voce law [25] (Voce ψ °):       1 exp p p s y        (10) Swift law [26] (Swift ψ °):     0 n p p s K       (11) Ludwick law [27] (Ludwick ψ °) :     0 n p p s K       (12) The parameters K and n for Hollomon's law The parameters σ y , α and β for the Voce's law The parameters ε 0 , K and n for Swift's law The parameters σ 0 , K and n for Ludwick's law R ESULTS AND DISCUSSION Experimental results igs. 1 and 2 respectively represent the uniaxial tensile and compression hardening curves for three different orientations: RD (rolling direction), TD (transverse direction) and ND (normal direction). By analyzing the curves in Figure 1 and Figure 2, we notice an anisotropy translated by the difference between the three directions. On the other hand, this anisotropy in normal direction (ND) for the two tests is different from that of the other directions which translates the phenomenon of asymmetry between traction and compression encountered in magnesium alloys. The yield and flow stresses for ND compression curve followed similar characteristics as in-plane tension at RD and TD directions. The yield stresses for RD are lower than those for TD and ND . F