## 2 Materials and Methods
* Steel S275 JR at \(-\)50 \({}^{\circ}\)C (see [19; 20; 22] for details on experimental procedures, material properties and critical loads), operating within the Ductile-to-Brittle Transition Zone (DBTZ), below the corresponding Reference Temperature [21] (T\({}_{0}=-\)26 \({}^{\circ}\)C). The material in such conditions is clearly nonlinear in tensile tests and moderately nonlinear in cracked conditions (CT specimens), with increasing nonlinear behaviour when the notch radius increases. Again, the thickness and the width of the fracture specimens were 25 and 50 mm, respectively. The fracture toughness results in cracked conditions do not fulfil K\({}_{\text{IC}}\) requirements and are qualified as K\({}_{\text{JC}}\)[20]. * Steel S275 JR at \(-\)10 \({}^{\circ}\)C (see [19; 20; 22] for details), operating within the Ductile-to-Brittle Transition Zone (DBTZ), above the corresponding Reference Temperature [21] (T\({}_{0}=-\)26 \({}^{\circ}\)C). The material in such conditions is, again and more noticeably, nonlinear in tensile tests, and moderately nonlinear in cracked conditions (CT specimens). The thickness and the width of the fracture specimens were 25 and 50 mm, respectively. Likewise, the fracture toughness results in cracked conditions do not fulfil K\({}_{\text{IC}}\) requirements and are qualified as K\({}_{\text{JC}}\)[20]. Thus, the materials covered in this analysis include two polymers, one composite with two different contents of reinforcement and two metals with different mechanical behavior (the steel been tested, additionally, at three different temperatures). Some of them are linear-elastic in tensile and fracture conditions (PA6 and SGFR-PA6 5 wt.%); some of them are linear elastic in cracked conditions and have a nonlinear stress-strain tensile curve (SGFR-PA5 50 wt.%, PMMA, AI/075-T651 and S275 JR at \(-\)120 \({}^{\circ}\)C); finally, some of them are nonlinear in both tensile and cracked conditions (S275 JR at \(-\)10 \({}^{\circ}\)C and \(-\)50 \({}^{\circ}\)C), not fulfilling linear-elastic fracture conditions in the fracture tests performed on cracked specimens. Thus, the variety of nonlinearity levels presented by the materials covered in this work represents a significant sample of engineering materials. Except for the AI/075-T651 [12], the EMC-ASED criterion has not been applied by the authors to the materials gathered in this work. Figure 1 shows a schematic of the different situations for the two extreme conditions, tensile tests (stress-strain curves, \(\sigma\)-\(\varepsilon\)) and fracture tests on cracked specimens (load-displacement curves, P-\(\Delta\)), with the fracture tests performed in notched conditions having an intermediate behaviour. Table 1 gathers the main material properties and parameters. assumes the following [PERSON]'s power-law equation for the tensile stress-strain relationship in the plastic region:  
\[\sigma=\mathrm{K}\varepsilon^{n}\mathrm{p} \tag{1}\]  
The parameters \(\sigma\), \(\varepsilon_{\mathrm{P}}\), \(\mathrm{K}\), and \(\mathrm{n}\) are the true stress, the true plastic strain, the strain-hardening coefficient and the strain-hardening exponent, respectively. Then, the EMC computes the total strain energy density (SED) for the real ductile material up to the peak point (i.e., the ultimate point) in the stress-strain tensile curve. Finally, it assumes that the equivalent (virtual) brittle material develops the same amount of tensile SED for brittle fracture to take place. These basic assumptions allow the tensile strength of the equivalent material to be computed as a closed-form expression. The Strain Energy Density (SED) of a ductile material is the area under the curve until the beginning of the necking starts to take place (maximum point of the stress-strain curve; see Figure 2a).