Abstract This study examines crack initiation and propagation in AISI D2 punch tools subjected to cyclic and impact loading using the Finite Element Method (FEM) and the Extended Finite Element Method (XFEM). FEM analysis is employed to identify stress concentration areas and potential failure points, while XFEM facilitates efficient simulation of crack growth paths without the need for re-meshing. The Johnson–Cook constitutive and damage models are applied to accurately capture the elastoplastic behavior and fracture characteristics of AISI D2 under realistic industrial punching conditions. Results show that crack evolution occurs in distinct stages, from stable propagation to catastrophic failure, closely linked to Von Mises stress and plastic strain accumulation. These numerical predictions are corroborated by microstructural observations in failed punch head. The study also highlights the superior ability of XFEM to predict crack trajectories compared to conventional FEM, providing valuable insights into fracture mechanisms. The findings offer practical guidance for improving punch tool design through geometry optimization, material selection, and surface engineering. Furthermore, this research emphasizes the critical role of predictive numerical modeling in extending tool life, minimizing downtime, and enhancing reliability in industrial sheet metal forming processes.
Reinforced concrete (RC) structures are susceptible to crack initiation and propagation during service, making accurate numerical simulation of crack behavior essential for assessing structural durability and safety. Current numerical approaches for simulating concrete cracking include smeared/continuum approaches, extended finite element method (XFEM), phase-field methods, and meso-mechanical models. In particular, smeared/continuum approaches (e.g., smeared crack and plastic-damage models such as CDP) indirectly reflect cracking through diffusive damage fields without providing explicit geometric information on crack locations and propagation paths. The XFEM module in commercial software is further restricted to first-order elements and encounters difficulties in simulating multi-crack propagation. These limitations indicate that further development of complementary crack-simulation frameworks is warranted. To this end, this paper presents a cracking simulation framework for RC members within the theoretical framework of the Specified Stress Method, adopting an adaptive degree-of-freedom strategy to balance computational accuracy and efficiency. The method introduces inelastic strain as an additional unknown and establishes a variational principle and the corresponding virtual work equation. Concrete cracking is described by specifying the stress on the crack plane to zero, so that the crack-surface stress remains zero after cracking, thereby avoiding the issue of damage reversibility and improving computational convergence. The method requires neither a predefined crack path nor remeshing after cracking. Unlike smeared/continuum approaches that rely on diffusive damage fields, the crack propagation paths, distribution characteristics, and evolution of multiple cracks are characterized through the spatial distribution of cracked integration points within the finite element mesh. In the present implementation, crack initiation is governed by the maximum tensile stress criterion, and a linear elastic constitutive model is adopted for concrete as a deliberate simplification to establish and verify the core computational mechanism of the framework. The proposed method was examined through three numerical examples. First, comparison with theoretical solutions confirmed the algorithm’s correctness in simulating cracking in heterogeneous RC tension members. Second, comparison with experimental results demonstrated qualitatively consistent crack propagation trends and load–displacement responses for RC beams under mixed-mode cracking; the calculated ultimate load of the plain concrete beam is lower than the experimental value, which is attributable to the use of the maximum tensile stress criterion without fracture energy considerations, and certain crack morphology deviations are observed due to the neglect of reinforcement–concrete bond-slip. Third, a multi-crack simulation of an under-reinforced RC beam showed that, whereas the XFEM module in ABAQUS captures only a single dominant crack near the mid-span, the proposed algorithm predicts multiple distributed cracking zones on both sides of the mid-span, qualitatively consistent with the typical flexural cracking behavior of under-reinforced RC beams; the algorithm also supports second-order elements (e.g., C3D20R) unavailable in the ABAQUS XFEM implementation. While the method is still in an exploratory stage, these results confirm the feasibility and potential of the Specified Stress Method as a complementary framework for RC cracking simulation, providing a basis for further development.
Xiaoqing Zhang, Jialin Wang, Zhijian Yi et al.· Materials· 0 citations
This study investigates the fracture behavior of pressure equipment under static loading by comparing analytical solutions, conventional FEM, and XFEM. Cylindrical and spherical structures with semi-elliptical surface cracks are analyzed to evaluate the effects of crack geometry and structural curvature on the stress intensity factor (KI). Results show that XFEM accurately captures crack behavior without complex remeshing, closely matching analytical solutions (deviation <1%), whereas FEM reliability depends strongly on mesh refinement near the crack. The stress intensity factor increases with relative crack depth (a/t) and structural curvature (decreasing R/t), with spherical structures exhibiting higher KI than cylindrical ones. Overall, the study demonstrates XFEM's efficiency for assessing structural integrity and guiding the design of safer pressure equipment in energy and environmental applications.
Jamila Bouchgl, A. Hachim, Khadija Ouaissa et al.· E3S Web of Conferences· 0 citations
Cracks starting at corner features are the critical consideration for gas turbine manufacturers when demonstrating the damage tolerance of discs to satisfy regulatory requirements. Little has been published on this crack type, however, beyond the derivation of geometry correction factors. This work therefore studies closure, overload and high temperature effects in corner cracks using finite element (FE)analyses, representing the crack tip as a sharp notch and including the effects of plasticity and creep. Meshes for 2D edge and 3D corner cracks were generated using Microsoft Excel macros, enabling models to be built very quickly with precise control of element geometries. Geometry correction factor polynomials were derived for a wide range of corner crack test piece designs that account for the constraints imposed by their threaded ends. The FE work then studied closure, highlighting the role of crack flank plastic strains on the closure mechanics. Closure predictions were compared with experimental Potential Drop voltage-load measurements from selected loading cycles. The evolving stress-distance profiles as the crack grows following an overload were simulated by removing arcs of elements ahead of the crack tip. The predicted durations of the overload effects were in line with classical theory for 2D edge cracks, although in corner crack testing the retardation behaviour persisted for much longer than suggested by the models. At high temperatures, creep crack growth was simulated by again removing arcs of elements, this time when a critical fraction of the rupture life was exceeded. This technique was used to explore the conditions under which creep-dominated time dependent crack growth occurs. Finally, a method was developed for calculating growth rates based on the low cycle fatigue damage accumulated ahead of the moving crack tip. Predictions for different R-ratios agreed well with experimental data, and the application of the model to overloads was demonstrated.
This study aims to numerically investigate the mode I, II, and III fracture behaviors of additively manufactured degradable, bioplastic polylactic acid (PLA) lattice specimens. Numerical simulations were performed using the eXtended Finite Element Method (XFEM) based on the extracted PLA's mechanical and fracture material properties. The maximum principal stress and fracture energy power‐law criteria were utilized to simulate damage initiation and evolution in three‐dimensional (3D) numerical analyses. To consider the effects of build orientation, the transversely isotropic elasticity model (TIEM) was implemented. To facilitate the XFEM analyses, the equivalent solid material model (ESMM) technique was also utilized. The experimental load‐displacement responses of single‐edge notched bending specimens under the symmetric and asymmetric four‐point bending and mode III transverse shear cracked plate tests were conducted for comparison with the XFEM analyses in mode I, II, and III fracture, respectively. A common calibration factor, as well as the simultaneous utilization of the TIEM model, as well as the XFEM and ESMM techniques, reflected numerical results of acceptable accuracy compared to the experimental results; 5.3% (3.4%), 4.4% (5.8%), and 9.6% (5.4%) differences for the stiffness (peak load) of mode I, II, and III specimens, respectively.
Bahman Paygozar, R. Gorguluarslan· Fatigue & Fracture of En...· 0 citations
Conventional finite element methods suffer from critical drawbacks in simulating concrete crack propagation, including mandatory frequent remeshing, mesh distortion-induced numerical divergence and accuracy loss. Furthermore, robust crack evolution and autonomous crack path tracking remains challenging for existing algorithms. To overcome these limitations, this study develops a numerical model based on the Vector Form Intrinsic Finite Element (VFIFE) method for reinforced concrete (RC) shear walls. The proposed model adopts a discrete particle system, which eliminates the need for mesh rezoning and effectively avoids mesh distortion, and enables autonomous crack propagation direction selection via local stress-strain field judgment. The interaction between concrete and reinforcement across crack interfaces is represented using an equivalent interfacial spring formulation, which enables the evaluation of bond stress induced by crack opening. Comprehensive quasi-static tests were conducted on nine RC shear wall specimens with varying axial compression ratios, reinforcement ratios and aspect ratios for model validation. Numerical results show good agreement with experimental observations in crack patterns, propagation paths and damage distributions. Simulated horizontal crack heights have errors within 5%, and diagonal crack heights within 10%. The model also accurately captures crack opening widths and evolution of local bond stress induced by crack opening. Parametric studies show that higher axial compression and edge reinforcement ratios suppress crack growth, while larger aspect ratios promote cracking. Compared with conventional crack-tracking finite-element methods, the proposed VFIFE model maintains stable crack propagation through particle splitting and interfacial-spring mechanism without remeshing or global stiffness-matrix reconstruction, thereby reducing mesh-intervention cost and preserving crack-path accuracy. This VFIFE-based approach features high efficiency and stability, serving as a reliable tool for damage assessment and performance analysis of RC structures.
Hongmei Zhang, Yangyang Bao, Yuanfeng Duan et al.· International Journal of Str...· 0 citations
Rigorous application of continuum damage mechanics (CDM) models coupled with crack propagation schemes can predict crack branching or zigzag trajectories near the crack tip, even when the macroscopic crack growth is straight. This arises from oscillations in the local damage field and is consistent with experimental observations of ductile tearing; however, it complicates finite element simulations. This study investigates this behavior through two crack propagation strategies in finite element simulations. The first, termed the Mesoscale Crack Advance (MCA) approach, explicitly tracks changes in crack trajectory based on the evolving local damage field. The second, termed the Process Zone Element (PZE) approach, represents damage and crack advance in an averaged sense over a material's characteristic length. Both approaches produce similar results. Despite its simplified formulation, the PZE approach captures the essential features of ductile crack propagation and provides a computationally efficient, practical alternative for simulating ductile crack growth and brittle fracture.
A. Ziccarelli, A. Kanvinde, G. Deierlein· Fatigue & Fracture of En...· 0 citations