Ductile fracture is commonly considered as a mechanical response of nucleation, growth, and finally, coalescence of voids in metallic alloys induced by plastic deformation. Several micromechanical ductile fracture models and criteria have been developed within the past 50 years. In 1968, McClintock [1] established ductile fracture criteria for the growth of long cylindrical void under applied stress. Next year, Rice and Tracey [2] analytically modeled the growth of spherical voids in a tension strain field. In both cases, high-stress triaxiality increases the void growth rate exponentially. Later, Gurson [3] developed constitutive equations for porous materials using the upper bound theorem of plasticity. Gurson's yield criteria was based on the assumption of idealization of a single void in a rigid plastic cell (to represent matrix) in which the void volume fraction was defined as "f ". Similarly, Rousselier [4] proposed a macroscopic approach to predict ductile damage using the continuum thermodynamics. Also, Lemaitre [5] put forth a model for ductile fracture in the framework of thermodynamics: effective elasticity modulus, which decreases with an increase in the damage.Chu and Needleman [6] published a void nucleation model employing Gurson's yield criteria. Next, Tvergaard [7,8] conducted a bifurcation analysis on the shear band instabilities and void coalescence in localized shear bands in a continuum model with a void-matrix aggregate proposed by Gurson. Later, Tvergaard and Needleman [9] carried out a finite element analysis for the coalescence of voids and introduced a modification to the yield condition. After the modifications to Gurson's constitutive equations, the model is called as "GTN model" and enabled to predict ductile damage in metals. Researchers have carried out numerous studies to model ductile fracture for different applications, including tensile testing, [10][11][12][13][14][15] formability limit diagrams, [16][17][18][19][20] small punch tests, [21][22][23] electromagnetic impaction, [24] Charpy V-notch test, [25,26] bending, [27][28][29] tube hydroforming, [30,31] roll forming. [32] The constitutive equations of the GTN damage model require nine different parameters. In the literature, scholars determined these parameters with different methods for various materials. Ali and Huang [33] utilized a statistical approach, response surface methodology (RSM), to estimate damage for AZ61 Mg alloy. They coupled a finite element model (FEM), which is developed in ANSYS and evaluated the response of each variable on the regression model coefficients. Their approximation algorithm compared the results of each increment with the experimentally obtained tensile test results that initially start with the literature values for different materials, including steel, titanium, and aluminum alloys. Similarly, Abbasi and colleagues [34] determined GTN model parameters by RSM for the tailor-welded monolithic interstitial free (IF)-steel blanks. They compared the results of FEM, which was constructed on the...
