## 5 Conclusions  
A simplification of the testing phase required for material ductility evaluation and for ductile damage models calibration was achieved using specific specimen geometries, originally proposed by [PERSON] and by [PERSON], modified and used to induce multiaxial tensile-shear stress states employing a common uniaxial testing machine as equipment, only. This study showed that the approach can successfully replace more complex and expensive testing normally performed for damage model calibration. An experimental campaign was conducted to test different configurations of the proposed samples on a 17-4 PH steel and a Ti6 Al4V titanium alloy. Three state-of-the-art ductile damage models were calibrated using conventional tests as well as tests based on [PERSON] and [PERSON]'s specimens. The main findings of this article are summarised below:  
* The [PERSON] and [PERSON]'s test specimens are capable of generating several mixed tensile-shear stress states in a low triaxiality regime using only a uniaxial testing machine; \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline
**Ti6 Al4V** & \multicolumn{3}{c}{**MMC**} & \multicolumn{3}{c}{**CC**} & \multicolumn{3}{c}{**HC**} \\
**Test** & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & **SDErr** & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{\beta}\) & \(\mathbf{\gamma}\) & **SDErr** & \(\mathbf{a}\) & \(\mathbf{b}\) & \(\mathbf{c}\) & **SDErr** \\ \hline Driemeier & 0.079 & 692.4 & 0.03 & 0.82 & 1.50 & 0.853 & 1.000 & 0.04 & 1.00 & 0.80 & 0.550 & 0.05 \\ Mohr & 0.060 & 675.0 & 0.08 & 0.81 & 1.55 & 1.080 & 1.000 & 0.03 & 1.00 & 0.68 & 0.020 & 0.07 \\ Conventional & 0.090 & 710.0 & 0.09 & 0.80 & 1.55 & 0.997 & 0.925 & 0.07 & 1.10 & 0.80 & 0.070 & 0.04 \\ Driemeier and Mohr & 0.060 & 673.9 & 0.07 & 0.81 & 1.55 & 1.470 & 0.850 & 0.07 & 1.00 & 0.74 & 0.036 & 0.15 \\ All specimens & 0.075 & 689.0 & 0.11 & 0.90 & 1.32 & 0.840 & 1.000 & 0.11 & 1.00 & 0.78 & 0.047 & 0.11 \\ \hline \end{tabular}
\end{table} 
Table 4: Calibration constants for TiAl4V alloy and standard deviation errors based on different combinations of inputs for the three damage models. The \(n\) parameter for the HC model is set equal to 0.1. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**17-4 PH** & \multicolumn{3}{c}{**MMC**} & \multicolumn{3}{c}{**CC**} & \multicolumn{3}{c}{**HC**} \\
**Test** & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & **SDErr** & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{\beta}\) & \(\mathbf{\gamma}\) & **SDErr** & \(\mathbf{a}\) & \(\mathbf{b}\) & \(\mathbf{c}\) & **SDErr** \\ \hline Driemeier & 0.013 & 742.0 & 0.14 & 0.51 & 1.02 & 1.970 & 0.750 & 0.09 & 1.02 & 1.36 & 0.017 & 0.12 \\ Mohr & 0.013 & 725.0 & 0.15 & 0.50 & 1.05 & 1.450 & 0.990 & 0.11 & 1.05 & 1.10 & 0.000 & 0.05 \\ Conventional & 0.020 & 751.0 & 0.13 & 0.53 & 0.85 & 1.130 & 0.986 & 0.11 & 1.03 & 1.42 & 0.020 & 0.11 \\ [PERSON] and Mohr & 0.010 & 721.1 & 0.12 & 0.50 & 1.03 & 1.240 & 1.000 & 0.10 & 1.00 & 1.38 & 0.015 & 0.20 \\ All specimens & 0.020 & 732.2 & 0.11 & 0.60 & 0.74 & 1.110 & 1.000 & 0.11 & 1.06 & 1.20 & 0.010 & 0.12 \\ \hline \end{tabular}
\end{table} 
Table 5: Calibration constants for 17-4 PH alloy and standard deviation errors based on different combinations of inputs for the three damage models. The \(n\) parameter for the HC model is set equal to 0.1. It is possible to vary the tensile-to-shear ratio of the stress state just by changing the machined geometry and dimensions ([PERSON]), or just by clamping the samples at a different angle (Mohr) through a purposely designed gripping system; The ductility of a 17-4 PH and of a Ti6 Al4V alloys could be estimated with the same accuracy level achievable using a more typical complex multiaxial testing and calibration procedure; The prediction effectiveness of the Modified Mohr-Coulomb, Coppola-Cortese, and Hosford-Coulomb damage models was investigated. Conceptualization, G.C. and L.C. ; methodology, G.C. and L.C. ; software, G.C. ; validation, G.C. ; formal analysis, G.C. ; investigation, G.C. and L.C. ; resources, L.C.