A cohesive zone model for fatigue under cyclic thermo-hydro-mechanical loading

A local comparison of the virtual crack closure technique and a cohesive zone model in calculating the strain energy release rate for large and curved delaminations

Equivalent cohesive zone modeling of the bonding performance of slab track interface with bubble defects: Theory, validation, and application

A modified irreversible cohesive zone model for predicting the fatigue debonding at laser-welded interfaces

Failure mechanics of carbon nanotube modified epoxy adhesives in co-cured composite T-joints: experimentally informed cohesive zone modelling

ABSTRACT In this study, the fracture characterisation under Mode I loading of Ti6Al4V alloy/carbon fibre reinforced polymer (CFRP) hybrid composites was investigated through mechanical testing and numerical simulations. Double cantilever beam (DCB) tests were performed to obtain the critical strain energy release rates (GIC) for the joints of Ti6Al4V/carbon fibre/low melt poly(aryl ether ketone) (CF/LM-PAEK) and Ti6Al4V-carbon fibre/poly (ether ketone–ketone) (CF/PEKK) composites. The Mode I interlaminar fracture energy (GIC) of the joints was evaluated using three different methods, including modified beam theory (MBT), compliance calibration (CC) and modified compliance calibration (MCC). The average GIC values of the LM-PAEK specimen obtained by the MBT, the CC and the MCC methods were 22.3%, 16.3% and 21.2% higher than that of the PEKK specimen. It shows that the LM-PAEK specimen had stronger adhesion than the PEKK specimen bonded with the Ti6Al4V sheet. Simulations were performed to investigate the interfacial behaviour of the Ti6Al4V/CFRP composites based on the cohesive zone model (CZM) using the LS-Dyna software. Results show good agreement between the experimental and the FEA results, with average errors of 2.28% for LM-PAEK and 4.36% for PEKK.

A quantification method to study material properties of pectin-enriched layers in wild-type (WT) Arabidopsis thaliana leaves is proposed here. In this paper, the mechanical and adhesive properties of this layer were investigated by measuring the response of deep needle insertion into the pectin-enriched areas of live leaf samples in WT Arabidopsis thaliana using two different conical probes. One was a commercial diamond tip with a radius of 5 μm, while the other was a sharp tungsten tip with a radius of 110 nm. The process was then modeled in ABAQUS using a cohesive zone model (CZM), which allowed the Young's modulus and fracture toughness to be quantified. Pectin exhibits a very low fracture toughness (<1.5 J/m2), yet it remains sufficient to maintain cell adhesion. The proposed method enables quantitative characterization of pectin properties across different mutants and developmental stages, offering new mechanistic insight into the role of pectin in morphogenesis.

The solidification of volcanic rock-like materials using cohesive zone models and finite element method

Actual microstructure-based FEM simulation of crack interaction in thick thermal barrier coating using cohesive zone models

Analytical study on bond interface damage mechanism of hot-cast anchorage using trilinear cohesive zone model

This study systematically investigates the low-velocity impact response of aerospace-grade carbon-fiber-reinforced polymer (CFRP) T-stiffened panels. Through drop-weight impact tests at 20 J and 35 J energies and Cohesive Zone Model (CZM) numerical simulations, a comparative analysis was performed on two composite configurations: the pure CFRP baseline (Configuration A) and the hybrid configuration incorporating surface glass fiber layers (Configuration B). High-fidelity correlation between experimental and numerical results was achieved, validating the progressive damage evolution of the matrix and fiber constituents. The main findings demonstrate that the hybrid Configuration B exhibits significantly superior impact resistance compared to the monolithic CFRP Configuration A. The introduction of surface glass fiber layers produces a synergistic hybrid effect in the composite system. This surface layer acts as a protective buffer, effectively attenuating the impact load before it propagates to the underlying carbon fiber laminate. As a result, the hybrid structure absorbs more energy and effectively suppresses rapid crack propagation. Under 35 J impact energy, Configuration B avoids the brittle failure of the matrix observed in Configuration A, achieving a 24% increase in permanent energy absorption. This surface hybridization strategy provides an effective method for improving damage tolerance and preserving the structural integrity of advanced composite stiffened panels.

Polymer insulation layers such as polyimide (PI) have gradually replaced inorganic dielectric layers (SiO2, SiCN) in the integrated packaging process of hybrid bonding (HB). PI can fill the gaps in the thermal compression bonding process and help to obtain a good Cu/Polymer bonding interface. At present, the existing post-crack double cantilever beam tensile test (PBC-DCB) has been successfully applied to the quantitative measurement of bonding strength of hybrid bonding with inorganic materials, but this method only considers elastic behavior. Since PI exhibits viscidity, elasticity and plasticity, knowing how to correlate these properties to the bonding process is challenging. Whether PBC-DCB is suitable for the characterization of PI bonding is unclear. This paper presents a comprehensive experimental and finite element analysis (FEA) study on the PI–PI bonding interface. Firstly, nanoindentation experiments and simulations are performed on the prepared PI interface to obtain key elasticity and plasticity parameters. Then, the bonding strength is characterized by the PBC-DCB test. Theoretical and experimental results show that the plasticity of PI causes energy dissipation during stretching, resulting in a deviation of approximately 2.51% compared with pure elasticity. Based on experimental data, the Cohesive Zone Model (CZM) FEA method is used to simulate the crack propagation. The results indicate that the Embedded Process Zone (EPZ) model can accurately describe crack initiation and delamination behavior, with a margin of error of about 3.61%. Finally, based on the EPZ CZM, defects such as bonding void and wafer warpage are further discussed in relation to bonding strength measurement.

The point-stress criterion (PSC) offers a practical approach for predicting the notched strength of polymer composites, but its reliance on an empirically fitted characteristic length limits its predictive generality. This study presents a physics-based modification of the Srivastava-style PSC, where is derived directly from the fracture process zone (FPZ) length obtained from cohesive zone modeling, eliminating the need for geometry-dependent empirical fitting of while requiring only a single calibration of constants and using a reference geometry. These constants remain fixed for all subsequent predictions across different hole sizes and specimen widths. A unified computational framework implementing constant and linear traction–separation laws is developed within a MATLAB environment. The optimal FPZ length is determined from the stationary point of the R-curve (), subject to a critical crack opening displacement cutoff. The framework is validated against comprehensive experimental data for a Glass/Epoxy laminate ( MPa) across a wide range of hole radii (0.3–20 mm) and specimen widths (10, 20, 40 mm). Results demonstrate that the constant cohesive law significantly outperforms the linear law, achieving an overall prediction accuracy of 84.7% (15.3% mean error) with an optimal FPZ length mm. The linear law yields slightly lower accuracy (82.9%, mm), while the exponential law is unsuitable for this quasi-brittle system. The proposed framework successfully captures size effects and finite-width dependence without empirical fitting of . By linking the characteristic length directly to cohesive zone mechanics, this work provides a robust, physically consistent, and predictive extension of the PSC for engineering design of notched polymer composite structures.

The fracture of bituminous polymer composites is fundamentally dictated by microstructural heterogeneity and the complex viscoelasticity of the asphalt matrix. This study develops a robust numerical framework coupling a random polygonal aggregate distribution algorithm with a bilinear cohesive zone model (CZM) to simulate fracture mechanics in heterogeneous asphalt-based composites. A key feature of the model is the explicit accounting for the stochastic distribution of the coarse aggregate and the time-dependent mechanical response of the fine aggregate matrix (FAM). Following experimental validation via frequency sweep and semi-circular bending (SCB) tests, a multi-scale parametric analysis was conducted to quantify the impacts of aggregate gradation, volume fraction, and shape. Results demonstrate that mixtures with high percentages of large-sized aggregates effectively delay macroscopic fracture by increasing the energy dissipation required for cracks to bypass the aggregate phase. While increasing the volume fraction of aggregates improves peak strength, it simultaneously accelerates post-peak load deterioration and reduces total fracture work, indicating a critical loss in the composite’s deformation capacity. Furthermore, particles with higher angularity provide superior blocking effects compared to rounded counterparts. This research offers a high-efficiency computational tool for the structural optimization of highly filled composites and provides critical insights into their internal stress states and macroscopic fracture mechanics.

In recent years, mixing an appropriate amount of flexible fibers(e.g., basalt fibers, polypropylene fibers, etc.) into concrete has become a common practice. Numerous engineering applications have shown that adding one or more types of flexible fibers not only significantly enhances the mechanical properties of concrete, such as flexural and tensile strength, but also markedly improves its durability by resisting sulfate and chloride ion attack and reducing crack formation. Building upon this practical significance, this study developed finite element models to investigate the pull-out behavior of basalt fibers and polypropylene fibers based on the unified phase-field theory (UPFT) coupled with the cohesive zone model (CZM). The fiber-matrix interfacial adhesion was simulated using zero-thickness cohesive elements to investigate and analyze the adhesion performance of the two fiber types pulled out from the concrete matrix. A series of numerical simulations was conducted to evaluate the effects of embedment depth, fiber diameter, and interfacial properties on the mechanical response. The predicted pull-out loads exhibited good agreement with experimental results, confirming the reliability and accuracy of the proposed modeling framework. The findings indicate that the peak pull-out load of both basalt and polypropylene fibers increases with greater embedment depth and larger fiber diameter. Furthermore, enhancing either the interfacial adhesion strength or the matrix strength significantly improves the reinforcing effectiveness of the fibers within the concrete matrix.

The scientific literature increasingly supports the use of computational models to predict fracture across a wide range of applications, which, when calibrated with experimental data, can yield highly consistent results. Although the extended finite element method (XFEM) is widely used in commercial packages, phase field (PF) methods have emerged as a robust alternative. In this study, a cohesive zone model (CZM) was implemented using both approaches (a PF model with an implicit damage initiation criterion and a standard commercial XFEM solver with an explicit damage initiation criterion) to analyze their robustness and computational efficiency. First, a standardized fracture test of a compact tension (CT) specimen was simulated and compared with experimental data to validate both methods, achieving accurate predictions under plane strain conditions with a dominant mode I fracture behavior. Subsequently, the application of both fracture models was extended to flexible thoracic prostheses across two distinct chest wall reconstruction scenarios: a single-rib unilateral model and a multi-rib bilateral configuration. An extreme-case compressive displacement was assessed to identify critical regions susceptible to fracture initiation and to evaluate the structural limits of the proposed designs. The results showed that the PF approach required a higher computational time, but exhibited more stable convergence. In contrast, the XFEM-based solver required careful mesh calibration to ensure convergence under complex conditions. These results highlight the potential of the PF approach as a practical tool for identifying and improving critical regions of implants, overcoming the limitations of commercial XFEM implementations.

Degradation of glass fibre composites in fatigue: A cohesive zone model approach

During the production, storage, and use of solid rocket motors, the impact generated by unexpected accidents, such as collision or drop, will cause damage to the propellant and affect the safety of the motor. However, the progressive evolution mechanism of mesoscopic damage in NEPE propellant under such impact conditions has not been fully elucidated, and there is still a lack of quantitative method to evaluate the impact-induced damage degree, which restricts the engineering safety assessment of solid rocket motors. To investigate the influence mechanism, the mesoscale damage characteristics of NEPE propellant under drop-weight impact is systematically studied. First, damaged NEPE specimens are obtained by conducting drop-weight experiments with a 10 kg hammer, where the drop height is varied to apply different impact impulses. The internal meso-structure of the propellant is then characterized using micro-CT, yielding detailed imagery of the refined meso-structural features and damage morphologies in the NEPE propellant. To capture the dynamic evolution process of mesoscale damage, a mesoscopic model incorporating AP, Al, HMX particles and voids, is subsequently constructed based on the high-precision mesoscopic morphology characterized by micro-CT. By integrating the deviatoric constitutive model, Gurson plastic damage model, and bilinear cohesive zone model, high-fidelity numerical simulations of the drop-weight impact damage process are performed using the advanced SPH-FEM coupling algorithm. The results indicate that no significant damage occurs when the impact impulse is less than 13.85 N·s. As the impulse increases, phenomena including matrix microcracks, void collapse, particle/matrix interface debonding, and main crack formation appear sequentially. When the impulse exceeds 24.25 N·s, particle fragmentation and transgranular fracture occur, accompanied by plastic flow and frictional heating that induce ignition. Finally, the overall damage degree is fitted by the Boltzmann function, and a function for quantitatively describing the damage degree is obtained, which can provide theoretical support for the impact safety assessment of solid rocket motors.

This study primarily examines the strength of a single lap joint having a mixed adhesive overlap consisting of a single adhesive and its thermoplastic reinforced state under varying temperatures. In the single lap joint, Titanium-Boron reinforced A356 aluminum was employed as the metal adherend, while plain woven glass fiber-reinforced epoxy (GFRE) was employed as the composite adherend. In the application of the mixed adhesive overlap, the brittle adhesives were employed in the middle section of the lap joint, while the reinforcement of the thermoplastics was employed on the adhesives at both sides of the lap joint. The single lap joints were subjected to tensile tests at 1 mm/min loading rates under room temperature and 120 °C, which is the melting point of the copolyester. In the numerical analysis, the cohesive zone model was applied in order to define the adhesives; however, elastic isotropic and orthotropic material behaviors were employed for the metal and composite adherends, respectively. Eventually, it is determined that the strength of a mixed adhesive lap joint consisting of a single adhesive and its thermoplastic reinforced state is better than a lap joint made with the mono-adhesive alone. Although literature suggests that mixed adhesive overlaps can be formed using at least two different adhesives (one ductile and one brittle), this study demonstrated that a mixed adhesive zone can be created using a single adhesive and thermoplastic reinforcement.

Abstract This study presents a numerical investigation of the failure load of curved composite beams subjected to four-point flexural loading. Two key parameters were separately considered: (1) the stacking sequence and (2) the curvature radius of the composite beams. Delamination, identified as the predominant damage mode in curved composite laminates, was modeled in Abaqus® using the cohesive zone model (CZM). Additionally, failure loads and load–displacement curves were generated for comparative analysis. Beams with a higher number of unidirectional layers demonstrated greater critical bending loads. Specifically, the [0] 20 sample exhibited the highest predicted failure load of 590.3 N, compared to 484.0 N for the [0/90] 5S sample and 455.8 N for the [45/0/− 45/90/0] 2S sample. Furthermore, the failure load increased significantly with larger curvature radii, ranging from 3.0 mm to 12.0 mm with 3.0 mm increments. The predicted failure loads were 394.8 N, 555.8 N, 782.4 N, and 1010.8 N for radii of 3.0 mm, 6.0 mm, 9.0 mm, and 12.0 mm, respectively. The simulation results showed good agreement with previous experimental data. Overall, the findings confirm that the CZM approach is effective for analyzing the out-of-plane strength of curved composite beams.