## 1 Introduction  
High-strength low-alloy (HSLA) structural steel keeps increasing remarkably due to its equivalent weight to strength ratio to meet specific structural strength, particularly in machinery and offshore industries where fatigue loading is prevalent. The failure in steel structure subjected to cyclic loading often arise from surface defect induced by manufacturing processes that could nucleate crack. Several studies of test data obtained for steel and a few other materials require a comprehensive material parameter that affects crack growth [1; 2; 3]. Recently, the viability of the computation approach is replacing the destructive, time-consuming and expensive methods in structural integrity assessment-related decisions. Many factors influence fatigue crack growth (FCG) in structures, the stress intensity factor (SIF) in the crack front is a significant parameter in the prediction analysis using linear elastic fracture mechanics (LEFM). Hence, an accurate evaluation of SIFs is extremely important. Furthermore, The Griffith theory allows for a limited amount of plasticity at the crack tip as the energy release rate (G) leads to the same results as the SIF in linear elastic condition proposed by [PERSON] in steel [4]. Over the years, numerical methods provide a more accurate approach to extract the SIFs. However, crack front shape in finite element (FE) analysis is still a challenge with error percentage far beyond the experimental solutions [5,6]. The geometry changes as the crack progress is ensured with adaptive remeshing techniques in FEM in SIF [7]. The accuracy depends on effective meshing and sensitivity of the crack front shape and smaller crack growth increments. The virtual crack closure technique (VCCT) option offers a simpler but more general way for obtaining the energy release rate estimation in crack propagation at the crack tip which requires additional post-processing procedures with more precise results [8,9]. [PERSON] and [PERSON] [10] proposed VCCT in two-dimensional finite element stress intensity analysis with a coarse grid for modes I and II. The method is performed with constant strain elements using nodal forces and nodal displacements, the results were poor when with higher-order elements. [PERSON] et al. [11] developed [PERSON]'s theory for three-dimensional bodies applied in the finite element method. However, not all conventional FEM meshing tools can perfectly compute the SIF because the singularity near the crack tip fields. Consequently, very fine meshes are appropriate near the crack tip [12]. Research efforts on three-dimensional FEM based on VCCT are rare despite suggestions of the crack faces model using the iso-parametric for three-dimensional crack analyses [13]. [PERSON] [14] describes the algorithm process for 3D VCCT implementation with brick elements in FE analyses using quarter-point singular finite interface elements. The pre- and post-processing database is stored and accomplished in Patran FE software providing solid modelling, meshing and analysis setup. At the same time, Nastran code is used as the FE solver to execute the VCCT. [PERSON] et. al. [15] implemented the numerical LEFM analysis of energy release rate in 3D VCCT with various a/W ratio using self-developed FEM code with the first-order tetrahedral elements. The stable crack analyses result under Mode-I condition showed good applicability apart from the long-cracked geometries. [PERSON] and [PERSON] describe the 3D implementation of fatigue crack growth rate with planar crack [16]. Several numerical efforts such as the feature-preserving discretization paired with a local refinement approach adopted to capture small geometric features and locally resolve regions of damage propagation have showed improvements in the efficiency and accuracy of singularities [17]. Other interesting numerical tools for addressing similar challenges emerge in FE-based techniques, such as meshfree peridynamic methods that discretize areas into nodes, each with a defined volume in the reference configuration.