## 1 Introduction  
Ductile fracture accompanied by a remarkable amount of plastic deformation has been observed in a large number of steel structural components in buildings damaged by the Northridge (1994) [1] and Kobe (1995) [2] earthquakes. Fracture has been mainly described through the comparison of the strength obtained in the material testing against empirical stress capacities in civil engineering [3; 4; 5]. However, occurrences of such events have motivated researchers to study the ductile fracture mechanism, which had been of interest among the community of mechanical, aerospace, and nuclear engineers.  
The micromechanics-based fracture models involving the changes in micro-void of steel material during the fracture process (nucleation, growth, and coalescence) can be classified into two main categories: the coupled model that considers the internal damage evolution and accumulation, and the uncoupled model that considers only the effect of the fracture threshold (equivalent stress, strain, etc.) on critical fracture. The coupled model proposed by [PERSON] (1977) [6] has been widely used in structural engineering for the assessment of structural integrity. This model was further modified by many independent researchers to replicate the physical mechanism of ductile fracture under various stress states. Another type of coupled model is the continuum damage mechanics (CDM) model, which originated from the macroscopic damage variable proposed by [PERSON] (1958) [7]. The main drawback of these coupled models is that a considerable number of parameters need to be identified. A good example is the modified [PERSON] model [8] that has nine parameters, which increases computational cost and thereby limits the industrial application.  
In contrast, the uncoupled models have fewer model parameters and have been found in recent studies to provide comparable accuracy in predicting the ductile fracture behavior in comparison to the coupled models. In this sense, the model could be appropriate for application in civil engineering that requires large-scale structural simulation.  
The most representative of the uncoupled model is the [PERSON] (1969) model [9], which has been coded into the commercial finite element analysis (FEA) software ABAQUS [10], known as \"Ductile Damage\". The model is dependent on the stress triaxiality, \(\eta\), which is defined as the ratio of hydrostatic pressure to von Mises equivalent stress. It is assumed that the ductility decreases exponentially with the increase in stress triaxiality. This model implicitly indicates that the fracture strain in pure shear is higher than in uniaxial tension. In contrast to such belief, recent experimental reports [11] showed that the reverse is true in some cases. Therefore, stress triaxiality-dependent models may not be applicable in low or negative triaxiality domains where the shear fracture dominates. To overcome this issue, the lode angle parameter related to the normalized third deviatoric stress invariant has been incorporated into the recent fracture model [12; 13; 14]. The fracture locus is constructed in the 3D-space of equivalent fracture strain, stress triaxiality, and lode angle parameter.  
The objective of the present paper was to investigate the ductile fracture response of mild structural steel and to present the finite element method to simulate ductile fracture in structural components. Three types of specimens taken from structural steel SS275 plate were tested, in which ductile fracture was initiated under different stress states. The entire fracture responses of these specimens were simulated using the ABAQUS software [10]. The uncoupled fracture model proposed by [PERSON] (BW) [11] was selected to define the onset of fracture initiation. The detailed calibration methodology of the fracture parameters is presented with the results of digital image correlation (DIC) analysis and finite element (FE) analysis.