*3.6. Evolution of Young's Modulus*

From microhardness indentation tests, values of Young's Modulus E of all materials and treatments can be evaluated too. They lie between 32–50 GPa (Table 5) considering all materials, but within one material they did not change by more than 18% due to the different treatments. Mg5Zn0.3Ca and Mg0.3Ca showed moderate differences of Young's modulus at a strain of γ*T*~8. Mg5Zn0.15Ca0.15Zr had a variation of Young's Modulus at a strain of γ*T*~2. Pole figures (002) (010) (011) and (102) of the samples with apparent variations of Young's modulus during processing history were determined by XRD, displaying the crystallographic textures of the materials (Figure 14). From the latter, data of Young's Modulus could be simulated (Figure 15 for Mg5Zn0.3Ca): each obtained texture was discretized and represented as a result from 100,000 grains all having the same weight. Based on the orientation of each grain and the compliance constants Sij, the individual Young's modulus of each grain was calculated using Bunge's interdependence [50] of Young's modulus E with the materials' compliances Sij, and with the texture components. Using Voigt's average [51] for the E-values of all grains, an upper limit for the macroscopic E could be calculated. More details of the simulation have been given in publication [10]. The following compliances given in [52] for dilute Mg-alloys were used: S11 = 0.0172738 GPa<sup>−</sup>1, S12 = <sup>−</sup>0.01606 GPa<sup>−</sup>1; and S44 = 0.066667 GPa<sup>−</sup>1; neglecting influences from constituents Zn and Ca in higher percentages. These influences and the fact of upper-limit calculation may explain some positive, constant offsets of simulated values of E compared to the experimental values.


**Table 5.** Young's moduli of all alloys in various conditions.

**Figure 14.** Pole figures displaying crystallographic textures of Mg5Zn0.3Ca samples in the IS (furnace-cooled) and HPT-processed by 2 rotations (torsional strain γ*T*~8) and additional heat treatment at 100 ◦C for 1 and 24 h.

**Figure 15.** Comparison of measured and simulated values of Young's modulus data obtained from microhardness measurements and texture evaluations for Mg5Zn0.3Ca.
