Numerical and experimental study for AM50 magnesium alloy under dynamic loads

Magnesium alloys are widely used in automotive (steering wheel frames) and aerospace due to their lightweight, ductility, energy absorp tion and castability properties. Finite Element Analysis and design optimisation have driven the improvement of structural crashworthiness, stiffness, strength, durability, and NVH (noise vibration, harshness) performance, making it possible to meet both the safety requirements and weight reduction targets. The accuracy of the numerical methods is strongly dependent on the accuracy of the material models and parameters employed. This paper presents the numerical Simulation of the Charpy test for AM50 magnesium alloy. This standardised high-speed impact test method measures the energy absorbed by a standard specimen while breaking under an impact load. Numerical simulations were performed using Ansys LS-Dyna explicit solver combined with a Johnson-Cook material's law. Then a sensitivity study was performed using Ansys optiSLang to identify which of the input variables (JC parameters, test specimen's dimensions) has the most influence on the output variables (contact force and absorbed energy).


Introduction
Magnesium alloys were first used in the mechanical industry in aerospace construction [1]. Due to their excellent rigidity, ductility, and high strength-to-weight ratios, magnesium alloys increase their applications in various fields, from automotive to aerospace and biomedical engineering [2] [3] [4]. Likewise, magnesium alloys have been adopted for different structural and non-structural components [2] [5] [6] [7]. The investigations from [8] show that casting and subsequent hot rolling enables the production of magnesium alloy sheets containing grain refining additives. In as -cast conditions, all investigated additives increase the strength values compared to the base alloys. The effects of the solution treatment process and ageing treatments on the microstructure and mechanical properties of the AM50−4% (Zn, Y) alloy were investigated by Dai [9].
The investigations from [8] show that casting and subsequent hot rolling enables the production of magnesium alloy sheets containing grain refining additives. In as -cast conditions, all investigated additives increase the strength values compared to the base alloys. The effects of the solution treatment process and ageing treatments on the microstructure and mechanical properties of the AM50−4% (Zn, Y) alloy were investigated by Dai [9]. Both quasi-static and dynamic tests were conducted on different specimens die-cast, showing, in general, good ductility and capacity to absorb energy for AM50 Magnesium alloy [10]. The fatigue behaviour of AM50 was investigated in [11]. Dynamic fracture toughness of AZ61 magnesium alloy was investigated by Daud [12].
A numerical simulation of the behaviour of the magnesium alloy AM50 in tension and torsion was performed by Serban [13]. The advantages of the Johnson-Cook model over the linear elastic/plastic model are that it is easier to calibrate and determines shorter simulation times, but in terms of simulation accuracy, the linear elastic model with isotropic plasticity is optimal.
The purpose of this paper is to validate a numerical model of the Charpy test for AM50 magnesium alloy, considering the experimental results presented in the first part of the paper.

Experimental Material and Method
For the mechanical characterisation of the AM50 Magnesium alloy, specimens type 1 were used according to Fig. 1. Type 1 specimens with rectangular sections were used for tests under dynamic loading. The specimens were cast under pressure in the same conditions and technological parameters used to obtain the steering wheels. The experimental investigations are considered to be followed on Charpy impact. For this reason, the specimens were mechanically machined at the ends, and their shape became a parallelepiped, Fig. 2.  The specimens obtained were tested in two directions as follows: x In the z-direction (edgewise direction): denoted by W, having b ≈ 8 mm and h≈ 3 mm, respectively x In the y-direction (Flatwise direction): denoted by L, having b ≈ 3 mm and h≈ 8 mm, respectively. The tests were performed with the Charpy hammer of 25 J. The impact velocity was 3.8 m/s, and the striker was released from its initial position, an angle of 150º with the horizontal plane. The striking hammer capacity is 4 kN.
A specimen ready to be tested in the z-direction is presented in Fig. 3. The length of support was adjusted to 40 mm.

Experimental Results and Analysis
Following the tests performed, CEAST 9050 Pendulum Impact System allows the visualisation of different graphs that increase the understanding of AM50 magnesium alloy behaviour under dynamic loads. Impact Energy -Deflection curve, respectively Impact Force -Deflection curves obtained for the specimens tested in the z-direction are presented in Fig. 4 and Fig.5. Deflection is the displacement of the striker relative to the test specimen supports after impact, starting at first contact between striker and test specimen.  As observed in the figures above and table 2, most of the specimens have the same behaviour at impact, except the w5 specimen. The w5 specimen has a smaller cross-section, but at the same time, following the analysis of the breaking area, it could be seen that it has defects inside. If we exclude from analysis these values, it can be observed that the average of the impact energy is 5.49 J, the maximum average of the impact force is 1172 N, and the deflection at the break is 6.12 mm, respectively.
All the specimens have been break following the tests, Fig. 6. Results obtained for the specimens tested in the z-direction Impact Energy -Deflection curve obtained for the specimens tested in the y-direction are presented in Fig. 7. Only two specimens have been broken following the test (L1 and L3). The average deflection at the break is 20.12 mm, respectively 5.98 J is the impact energy for these specimens. The impact velocity reaches the value of 3.8m/s for our study. Current experimental results agree with Galatanu [10], who shows that the values of absorbed energy for 3m/s test velocity reached 5.45 J, respectively for 5m/s test velocity reached 5.82 J.
The results show, in general, good ductility and capacity to absorb energy for AM50 Magnesium alloy.
Furthermore, a validation of a numerical model was achieved considering the experimental results.

Numerical analysis 4.1 Finite Element model
An explicit FEA simulation of the Charpy test was performed using LS-Dyna Solver under Ansys Workbench. The FE model Fig. 9 was built considering the test specimens' entire geometry, but simplified ones for the impact hammer (striker) and supports. The geometry was discretised using first order, full integrated hexahedral elements of 0.5 mm. length, Fig. 10. Striker and supports were defined as rigid bodies, and DOF were blocked, except for the Z translation of the striker, to allow applying the initial velocity boundary condition. The numerical Simulation of the Charpy test was based on an impact hammer having a kinetic energy of 25 J, generated by a pendulum weight of 3.46 kg and an impact velocity of 3.8 m/s. The striker's density was numerically increased so that multiplied by the impact velocity, the impact kinetic energy of 25 J was achieved. Two load cases were computed. In the first one, the test specimens were impacted in edgewise direction Fig. 9a and then flipped with 90° Fig.  9b. a b Fig. 9. Numerical simulation Load cases, a -edgewise direction, b -Flatwise direction

Material Model
One of the most used material law in dynamic, highly non-linear simulation is the Johnson-Cook (J-C) strength model [14] coupled with fracture criteria. This isotropic elastoplastic law expresses material stress as a function of strain, strain rate and temperature. Assuming that the material is not temperature nor strain-rate dependent, the J-C parameters can be computed from the uniaxial tensile test, as follows: For the current analysis, J-C parameters were computed based on tensile test specimens with similar shape and size [2], shown in Table 3. The true stress-plastic strain is depicted in Fig. 11.

Numerical analyses results
Numerical analyses results, performed with nominal geometry dimension (8x3 mm) and J-C parameters described above, are shown in Fig. 12 and 13. One can observe that maximum contact force is overestimated, especially at the beginning of the simulation. At the end of the calculation, the velocity drop is also overestimated, suggesting that the numerical model is stiffer than in the physical experiment.

Sensitivity analyses
Sensitivity analysis studies how the variations in the input of a model influence the model' s output. Sensitivity analysis is used during the post-processing of simulation results to analyse the contribution of the input variable to the spread of each mode l response. Using the Metamodel of Optimal Prognosis (MOP) method in OptiSLang [15], the input variables in Table 4 were systematically changed by mathematical algorithms until a global optimum was identified.
The objective of this study was to minimise the contact force between the impactor and test probe, from 1400 N to 1200 N, as seen in experimental tests results (Fig. 5). Based on parameters from table 4, a Design of Experiments (DoE) scheme was automatically generated, with 60 samples. A target of 90% CoP was defined.

Sensitivity results
As seen in Fig. 14, the sensitivity analyses successfully reached convergence, and the target CoP of 90% was targeted. From the same plot, one can conclude that the geometrical dimensions of the test probe have the most influence on the contact force at impact. The Maximum_Tensile_Stress, the failure criteria embedded in the J-C material model, is the most influential non-geometrical parameter that drives the out response. In Fig. 15, one can see the approximate value of the objective (Contact force) regarding both input parameters. The support point, samples of the DoE matrix can be seen and investigated also.

Conclusions
The impact behaviour of AM50 magnesium alloy was investigated experimental and numerical. The experimental results for the Charpy impact test of AM50 magnesium alloy agree with those from the literature. Based on the quasi-static tensile test, the parameters for Johnson-Cook isotropic elasto-plastic material model were analytically calculated. Explicit numerical analyses were conducted to estimate the maximum force during at impact during the Charpy impact test. After the initial FEA results, a sensitive study was performed that proved that geometrical dimensions of the test probe and Maximum Tensile Stress are the most influential on the contact force at impact. Future work will focus on improving FEA correlation by investigating different failure damage limits for tensile and compression loads.