Issue 78

A. Gallo et alii, Fracture and Structural Integrity, 78 (2026) 489-503; DOI: 10.3221/IGF-ESIS.78.28

strain hardening, strain-rate sensitivity, and thermal softening. The homologous temperature ்ି்ೌ ೘್ି் ೘್்ೌ ೘೐೗೟ ranging from 0 (room temperature, T amb ) to 1 (melting temperature, T melt ) allows to take account of material strength reduction at elevated temperatures. The general relationship of JC model is given by: ௣௟ ൌ ൤൫ ൅ ௣௖ ௟ ൯൬ 1 ൅ ఌሶ ೛೗ ఌሶ ೛೗ , బ ൰ቀ 1 െቀ்ି்ೌ ೘್ି் ೘್்ೌ ೘೐೗೟ ቁ ௠ ቁ൨ (12) where σ pl is the plastic stress, A , B , C , and c are material parameters. Under quasi-static conditions and room temperature, the strain-rate and thermal terms vanish, and the expression reduces to: ௣௟ ൌ ൅ ௣௖ ௟ (13) where A represents the initial yield stress, B controls the magnitude of strain hardening, and c is the hardening exponent. Finite element simulations were conducted using ANSYS APDL 2024 R1 with a batch coupling to MATLAB to automate iterative parameters updating and objective function evaluation. At each iteration both numerical response and numerical derivatives are computed, and the error relative to reference experimental data for the ZK60 magnesium alloy [23,24] is evaluated. The geometry of analysed flat specimen with 2 mm thickness is shown in Fig. 2.

Figure 2 : Dimensions of tensile specimen of ZK60 magnesium alloy. Values are expressed in mm The finite element model was discretized using 8-node hexahedral SOLID186 elements, resulting in 78500 elements and 88638 nodes. After parameters identification procedure, a mesh convergence analysis was performed to provide satisfactory accuracy in global and local response while avoiding excessive computational burden. The FE static-analysis was conducted under 3D symmetry conditions, by modelling one eighth of the specimen, as shown in Fig. 3. The symmetry boundary conditions were applied to three orthogonal faces of the specimen (on planes , , ), while a vertical displacement ̅ of 3 mm was imposed on the sample bottom surface. The calibration was formulated as an unconstrained optimization problem, minimizing the difference between numerical and experimental engineering stress strain curve. The objective function was defined as follows: ሺ ሻൌ ׬ | ఙ ಷಶಾ ሺఌሻି ఙ ಶ೉ು ሺఌሻ | ௗఌ బ ഄ೎ ׬ ఙ ಶ೉ು ሺఌሻ ௗఌ బ ഄ೎ (14) where ிாெ ሺ ሻ and ா௑௉ ሺ ሻ represents respectively the numerical and experimental engineering stress-strain curves, while ௖ is the plastic strain corresponding to the necking onset. The considered optimization variables were: ൌቄ ቅ (15) Elastic properties of the ZK60 magnesium alloy, in terms of Young’s modulus E and Poisson’s ratio ν , were kept constant, focusing the optimization on the plastic parameters B and c only. The identified JC parameters were compared to the reference values reported in the literature as summarized in Tab. 1. It is worth noting that the objective function of proposed optimization scheme is at least one order of magnitude lower than outcomes from literature, thus providing with useful parameters for predictive analyses involving the ZK60 alloy.

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