## 3 Cohesive Model Applied to the SENT Specim in Tension  
The cohesive crack was initially introduced by [PERSON] [29] to model the nonlinearities that occur at the crack tip. The basic postulate of the model is that the singularity of the stress field vanishes because of the formation of a crack extension referred as the cohesive zone, capable of transmitting a given uniform tensile stress Y\({}_{\text{J}}\) between its two faces. Therefore, the stress intensity factor of the extended crack, referred to as a cohesive crack, becomes zero due to the contributions of the applied tensile load and of the stress Y, referred to as cohesive resistance. This condition determines the size of the cohesive zone. In the subsequent evolution of the model [30; 31], the cohesive resistance Y is no longer a material constant and is replaced by a material law; which determines a one-to-one relationship between the separation acquired by each pair of points of the cohesive zone coming from the same initial material point, and the tensile stresses of equal value and opposed sign that they transmit to each other. The Green function proposed by [PERSON] [22] allows for the cohesive model to be particularized for the SENT specimen in the view of obtaining the theoretical curves load-CMOD and J-integral--CMOD as a function of the cohesive resistance Y. The Green function G(x, a) is the stress intensity factor per unit load K\({}_{\text{P}}\)/p in a SENT specimen with a crack of depth a, when its faces are compressed by concentrated loads per unit thickness p applied at a depth x from the crack mouth. The superposition principle and the reciprocity theorem, as formulated by [PERSON] [23] for Hookean cracked bodies, allow the stress intensity factor K\({}_{\text{s}}\) and the crack opening field \(\omega=\omega(\text{x},\,\text{a})\) to be determined for any compressive stress distribution s(x) acting symmetrically on both faces of the crack (Figure 4a):  
\[\omega=\omega(\text{x},\text{a})=\frac{2}{\text{E}}J_{\text{x}}^{\text{a}} \text{G}(\text{t},\text{x})\text{K}_{\sigma}(\text{t})\text{dt} \tag{3}\]  
where E is the elastic modulus of the steel and plane stress has been assumed. The Green function proposed in [22] is:  
\[\text{G}(\text{a},\text{x})=\sqrt{\text{W}}\,\text{k}\Big{(}\frac{\text{a}}{ \text{W}}\Big{)}\,\,\text{h}_{2}(\text{a},\text{x}) \tag{4}\]  
Figure 3: (**a**) Schematic illustration for the CMOD determination from the pair of virtual VIC-2D extensometers of crack-opening displacements V\({}_{1}\) and V\({}_{2}\), respectively mounted on the speckle painted surface of SENT specimen at h\({}_{1}\) and h\({}_{2}\) depths; and higher-magnification images captured by VIC-2D equipment (VIC-2D, Correlated Solutions, Inc., South Carolina, SC 29063, USA) from a JFT-FIP test showing: (**b**) the test onset at an initial crack length, a\({}_{0}\); (**c**) a load instant with the marked crack length, a.  
where \(h_{2}(a,x)\) is the derivative with respect to the second variable of the given function \(h(a,x)\) is:  
\[h(a,x)=1-\Big{(}1-\frac{x}{W}\Big{)}^{2}\frac{2}{\pi}\text{arcos}\bigg{(}\frac{x }{a}\frac{W-a}{W-x}\bigg{)} \tag{5}\]  
and the factor \(k(a/W)\) can be obtained from the stress intensity factor \(K\infty\) of the SENT specimen when subjected to uniform stresses along the whole crack, \(s(x)=s\infty\), or equivalently, loaded in tension with remote stress \(s\infty\) far away from the crack.