Bilinear Traction-separation Law Research Articles

Process simulation of laser shock-based disassembly of adhesively bonded composite/metallic structural parts: a numerical upscaling

ABSTRACT In previous works, both experimental and numerical investigations have shown the potential of the laser shock technique for disassembling adhesively bonded composite/metal coupons. This study extends this concept to upscale the method, focusing on the full disassembly of a foreign object damage (FOD) panel designed to replicate an aircraft engine fan blade. Utilizing LS-Dyna explicit FE software, the numerical simulation incorporates various material models: a progressive damage model for the 3D CFRP substrate, Johnson–Cook plasticity model combined with Grüneisen equation of state for the titanium layer, and a cohesive zone model with a bilinear traction separation law for the adhesive layer. Investigating the FOD panel’s inclined geometry, a preliminary analysis examines the impact of inclination angles on shock wave propagation and back face velocity, revealing minimal alterations. Initial simulations are conducted to determine double pulse delay times and evaluate spot location effects. Automation of the multi-step process simulation is achieved through a Python script. After approximately 30 shots, complete disassembly of the FOD strip is achieved, with observed damage primarily limited to matrix cracking in the composite substrate. Numerical findings support the efficacy of the double-shot laser shock method for disassembling adhesively bonded metallic/CFRP components, contingent upon appropriate experimental arrangements.

Process simulation of laser shock-based disassembly of adhesively bonded composite/metallic structural parts: a numerical upscaling

ABSTRACT In previous works, both experimental and numerical investigations have shown the potential of the laser shock technique for disassembling adhesively bonded composite/metal coupons. This study extends this concept to upscale the method, focusing on the full disassembly of a foreign object damage (FOD) panel designed to replicate an aircraft engine fan blade. Utilizing LS-Dyna explicit FE software, the numerical simulation incorporates various material models: a progressive damage model for the 3D CFRP substrate, Johnson–Cook plasticity model combined with Grüneisen equation of state for the titanium layer, and a cohesive zone model with a bilinear traction separation law for the adhesive layer. Investigating the FOD panel’s inclined geometry, a preliminary analysis examines the impact of inclination angles on shock wave propagation and back face velocity, revealing minimal alterations. Initial simulations are conducted to determine double pulse delay times and evaluate spot location effects. Automation of the multi-step process simulation is achieved through a Python script. After approximately 30 shots, complete disassembly of the FOD strip is achieved, with observed damage primarily limited to matrix cracking in the composite substrate. Numerical findings support the efficacy of the double-shot laser shock method for disassembling adhesively bonded metallic/CFRP components, contingent upon appropriate experimental arrangements.

Crystal plasticity modeling of grain boundary softening and fatigue in U75V pearlite steel under low strain conditions: A study of cyclic rolling contact fatigue

Grain boundaries (GBs) exhibit fatigue-induced softening under low strain conditions, making them the weakest and most vulnerable regions within the material. This phenomenon significantly influences plastic deformation, plastic strengthening, and the initiation and propagation of microcracks, leading to material fatigue failure. This investigation presents a comprehensive model for the rolling contact fatigue (RCF) damage mechanism of U75V railway steel. Leveraging data from Electron Backscatter Diffraction (EBSD) and employing the Crystal Plasticity Finite Element Method (CPFEM), intragranular mechanical responses are elucidated. A modified bilinear Traction Separation Law (TSL) Cohesive Zone Model (CZM) is developed to capture the impact of GBs fatigue. Integrating this CZM with CPFEM, mechanical properties, scalar stiffness degradation (SDEG), fatigue damage factors, and crack evolution patterns are analyzed to explore the effects of grain morphology, orientation, GB angle, and area on GB fatigue damage and crack initiation. Results indicate a significant increase in GBs damage with increasing GBs angle or decreasing GBs area, highlighting the potential for reducing RCF damage through deliberate grain morphology design. Additionally, GBs are found to impede crack propagation, suggesting that grain refinement can mitigate crack propagation rates. This study enhances our understanding of intergranular fracture, mechanical responses, and microstructure evolution in U75V rail steel under cyclic rolling contact loading, offering novel methodologies for investigating metallic materials' deformation behavior concerning GB fatigue.

Progressive damage modeling in open hole composite laminates with ultrasound-informed drilling-induced delamination

Insertion of fasteners, often used in aerospace and automotive industries, requires drilling that induces non-uniform delamination between lamina of a carbon fiber reinforced plastic (CFRP). Understanding the effect of drilling-induced delamination on the mechanical performance and associated damage mechanisms (progressive damage and failure) is critical to ensure joining integrity. The present work develops an ultrasound testing (UT) method to quantify the drilling-induced delamination at each individual ply interface for CFRP laminates. We then develop a mesoscale finite element (FE) model of an open hole tension specimen by incorporating the UT-obtained drilling-induced delamination at each interface. This delamination is modeled using cohesive zone elements with a bilinear traction-separation law with progressive damage in each ply modeled using the 3D Hashin along with a progressive damage model. Our FE model, with UT-informed delamination, accurately predicts experimental observations of the stress concentration around the hole, damage progression, and open hole tension strength.

Numerical and experimental investigations of low-velocity impact on composite overwrapped pressure vessel with different stacking sequences

Composite overwrapped pressure vessels are designed to contain fluids that operate under high pressures. In addition to internal pressure, the design needs to account for out-of-plane loading in the form of low-velocity impact. In this study, a numerical analysis of four models of composite overwrapped pressure vessels with different stacking sequences is performed. A three-dimensional explicit finite element model using multi-layer stacked shell elements was used in the impact zone region to obtain reasonable computation time. Utilizing the bilinear traction-separation law, cohesive zone elements were used to simulate the delamination failure and as bonding between eight layers of CFRP covering the aluminum liner. The simulation results were then validated using drop-weight impact tests, which revealed that the response of contact force to impact time was comparable for both types of analysis. Prediction of failure was carried out by assessing the quantity of energy absorbed by the CFRP layers and was confirmed by shell element data that failed during simulations. In addition, the Hashin damage model confirmed that the matrix tensile failure mode was the predominant failure mode for all discussed impact scenarios. Model-A with Al + [90]8 stacking sequence was found to have the highest impact resistance based on the prediction of the composite’s failure area and the energy absorbed by the CFRP layers. Furthermore, it was found that COPVs with combinations of helical and hoop sequences tend to have larger areas of delamination due to high interlaminar shear stress between the CFRP layers.

Experimental and numerical investigation of the laser shock-based paint stripping process on CFRP substrates

Various laser shock wave applications have been proposed for metals; the most popular is the laser shock peening. In composites, the use of the laser shock wave technology is still at an early stage. Laser shock paint stripping (LSPS) is a method where a laser-induced shock wave is used to remove a paint from a substrate. In this study, a combined experimental–numerical study was performed on the LSPS on Carbon Fiber Reinforced Polymers (CFRP) substrates. Two types of specimens were investigated: specimens with an epoxy structural primer covered by a polyurethane base and a clear coat and specimens with the above layers plus an epoxy exterior primer between the epoxy structural primer and the polyurethane layer. The specimens were shot using various laser intensities aiming to obtain the stripping threshold and the stripping percentage as functions of the laser intensity. The diameter of the stripped area was measured by a profilometer. An electron microscope was used to evaluate the stripping efficiency. In parallel, a numerical model was developed using the LS-DYNA explicit Finite Element (FE) software. For the modeling of the CFRP, a progressive damage model with strain rate parameters was used while for the epoxy an elastic–plastic-hydrodynamic material model combined with the Gruneisen equation of state. The interface between these two materials was modeled using cohesive zone elements of zero thickness, which follow a bi-linear traction-separation law. Calibration of the modeling of the shock wave propagation inside the composite material was achieved through the comparison of the back-face velocity profiles, measured by a velocity interferometer system for any reflector system. The results from the multiple tests conducted revealed the repeatability of the process and the significant effect of the laser intensity. On the other hand, the model managed to predict well the back face velocity–time profile but in most cases, it failed to predict the stripping pattern. This is mainly due to lack of crucial material properties and the assumptions made in the modeling of the applied pressure profile.

Finite-element simulation of in-plane tear propagation in the dissected aorta: Implications for the propagation mechanism.

Computer modeling and numerical simulation are essential for understanding the progression of aortic dissection. However, tear propagation has not been properly modeled and simulated. The in-plane dissection propagation between concentrically distributed elastic lamellae is modeled using the cohesive zone method with a bilinear traction-separation law. The parameters of cohesive elements are calibrated for the three modes of interfacial damage in the media, enabling quantitative predictions of in-plane tear propagation. An idealized cylindrical tube-shaped bilayer thick-wall model of the aorta is employed to elucidate the influence of geometrical parameters, loading conditions and residual stress on the tear propagation. While the model is capable of replicating that deeper, larger tears are associated with lower critical pressure, new findings include: (i) Larger axial stretch leads to lower critical pressure; (ii) Increased magnitude of residual stress is associated with higher critical pressure; (iii) Pressure difference between true and false lumen alters the critical pressure; (iv) The interfacial damage is mostly opening mode in the axial direction, but shear-dominated in the circumferential direction; (v) Damage due to the opening mode is associated with smaller fracture energy, which makes it easier to propagate than the shear and the mixed modes. (vi) The deformed shape of the tear, which is related to its geometrical features and loading conditions, modulates the critical pressure via two pathways: (a) deformed shapes are associated with specific modes of damage, which influences the critical pressure, and (b) deformed shapes modulate the critical pressure directly via geometrical constraints.

A micromechanical damage-healing model for encapsulation-based self-healing polymer composites under tensile loading

In this study, a novel micromechanics-based damage model is proposed for the damage evolution of a two-component microencapsulated-based self-healing polymer composite. In this way, a representative volume element (RVE) including an epoxy matrix with randomly distributed poly(methyl methacrylate) (PMMA) microcapsules is modeled in DigimatTM software and analyzed in Abaqus®. A new technique is developed to investigate the progressive damage by pre-inserted cohesive elements along all element boundaries of the epoxy matrix, PMMA shell, and capsule-matrix interfaces with the bilinear traction–separation law. Moreover, the impact of interface bonding strength, interface fracture energy, and PMMA microcapsules volume fraction on the load-carrying capacity of the RVEs under uniaxial tension loading was studied. The results indicated that the tensile strength of the self-healing polymer composite increased as the interfacial strength and fracture energy increased from 10 to 60 MPa and 100 to 1000 J/m2, respectively. Furthermore, the higher volume fraction of 5% PMMA microcapsules results in a lower load-carrying capacity of self-healing polymer composite with a strength of 4.9 N. A similar trend of Young’s modulus was observed for microcapsule-loaded epoxy composite compared to the pristine epoxy matrix. The micromechanical model has proper accuracy in predicting the tension behavior of self-healing composite in comparison to experimental results. Finally, two healing strategies are considered for the damaged RVE.

Cohesive zone model based reliability analysis for a sandwich pipe

A cohesive zone model based reliability analysis for a sandwich pipe (SP) is presented in this paper. The collapse or burst strength of SP is predicted by a cohesive zone model based nonlinear finite element (FE) analysis. The interlayer adhesion is simulated by cohesive zone model in accordance with the maximum shear strength. The bilinear traction separation law is employed in the cohesive zone model. A quadratic stress criterion and an energy-based model are used for simulating the damage initiation and evolution. The validity of the FE analysis is then validated by the comparison between model prediction and experimental results. A first-order reliability method coupled with a response-surface method is then used for reliability estimate dealing with implicit limit state functions corresponding to failure modes of collapse and burst. A sensitivity analysis to investigate the influence of design variables on the reliability of SP is further conducted and the results show that working pressure, yield strength of material, and modelling uncertainties are relatively important design variables in predicting the collapse and burst strength of SP, while initial ovalities of internal and external pipes could be regarded as constants in the reliability analysis for improving the computational efficiency.

Degradation prediction of mode I cohesive laws of hygrothermally aged CFRP adhesive joint using a direct method and accelerated aging

AbstractA framework has been proposed to predict the mode I cohesive law parameters of degraded composite adhesive joint using direct method and accelerated aging tests. Double cantilever beam (DCB) specimens made with CFRP and epoxy were used to study mode I fracture. Accelerated and uniform aging was achieved using open‐faced specimens aged at 40°C and 82% relative humidity. Fracture testing of aged open‐faced specimens along with crack‐tip images were used to determine the degradation in traction‐separation law (TSL) with an aging. These correlations with bilinear TSL with aging were then used to develop a 3D finite element model of a closed DCB specimen that captures the nonuniform degradation across the specimen width. The TSL parameters degraded significantly at the edges compared with width center for closed DCB specimens. Reasonable agreement was observed between the predictions and the maximum load response of the closed joint.

Mesoscopic dynamic characteristics and RCF damage evolution of high-speed transmission gear in wind turbine

For the gears utilized in wind turbines, the main reason leading to malfunction is the crack initiation and propagation under cyclic loading. In the gear engagement process, the fatigue damage accumulates gradually and formulate visible microcrack if the fatigue parameter reaches to specified threshold. In order to simulate the fatigue evolution in wind turbine gears, a mesoscopic model is established, in which the Voronoi tessellation and cohesive elements are integrated, such that the crystal structure and grain boundary can be modeled. The dynamic stress distribution and fatigue evolution phenomenon are then investigated under different working conditions. The loading in the meshing region is simplified as moving load on a semi-infinite plane, so the shear stress distributions for per loading cycle are obtained. Furthermore, bilinear traction-separation law (TSL), Jump-in-Cycles (JIC) loading methodology and multi-axial fatigue criterion are involved to fulfill the damage accumulation simulation. As a result, the initiation location and propagation pattern of the fatigue crack are predicted, and the fatigue life curve is also obtained. Thereafter, the influence of wind speed and lubrication condition on fatigue damage evolution is also discussed. The results have shown that the wind loading mainly influences the magnitude of the maximum shear stress, whereas the contact width will determine the location of the maximum shear stress. When the whole fatigue evolution procedure is finished, the first two cracks initiate at the depth of 0.13 mm and 0.27 mm beneath the surface respectively, and then propagate into the substrate. Through comparative analyses of fatigue life curves, it can be concluded that higher wind speeds and poor lubrication conditions will reduce gear service life significantly.

Effect of lamina fiber orientation interfaced with semi-flexible adhesive layer on strength and failure mode of composite single-lap joints

Various geometric and material parameters such as adhesive thickness, adhesive overlap, adherend thickness, and composite layup may affect the strength of the joint under quasi-static loading and failure mode of bonded composite-to-composite single-lap joints (SLJs) and are investigated by previous studies. The study herein broadens these findings by looking into the effect of lamina fiber angle adjacent to the adhesive layer on the damage initiation and evolution in detail. In this regard, a composite-to-composite adhesively bonded SLJ with adherends made of E-glass/epoxy composites and [04//θ/03] (where//shows the adhesive location) layups are manufactured and tested under quasi-static tensile loading. The adhesive type is semi-flexible Araldite 2015. Experimental results show that by increasing the fiber angle from 0° to 90°, the shear stress in the adhesive layer is decreased while the peel stress is increased. In examining typical fracture interfaces for each layup configuration, a full description of failure mode assessment is obtained. In particular, the SLJ is modeled in Abaqus using cohesive elements with bilinear traction-separation law. Numerical results indicate that the bilinear cohesive law cannot model the exact load-displacement curve due to semi-flexible behavior of the epoxy adhesive, but it can predict maximum strength precisely. The failure of composite joints is significantly influenced by shear stress.

Development and Numerical Implementation of a Modified Mixed-Mode Traction-Separation Law for the Simulation of Interlaminar Fracture of Co-Consolidated Thermoplastic Laminates Considering the Effect of Fiber Bridging.

In the present work, a numerical model based on the cohesive zone modeling (CZM) approach has been developed to simulate mixed-mode fracture of co-consolidated low melt polyaryletherketone thermoplastic laminates by considering fiber bridging. A modified traction separation law of a tri-linear form has been developed by superimposing the bi-linear behaviors of the matrix and fibers. Initially, the data from mode I (DCB) and mode II (ENF) fracture toughness tests were used to construct the R-curves of the joints in the opening and sliding directions. The constructed curves were incorporated into the numerical models employing a user-defined material subroutine developed in the LS-Dyna finite element (FE) code. A numerical method was used to extract the fiber bridging law directly from the simulation results, thus eliminating the need for the continuous monitoring of crack opening displacement during testing. The final cohesive model was implemented via two identical FE models to simulate the fracture of a Single-Lap-Shear specimen, in which a considerable amount of fiber bridging was observed on the fracture area. The numerical results showed that the developed model presented improved accuracy in comparison to the CZM with the bi-linear traction–separation law (T–SL) in terms of the predicted strength of the joint.

Modelling of the intergranular fracture of TWIP steels working at high temperature by using CZM–CPFE method

Grain boundaries (GBs) of metallic materials will become the weakest and most vulnerable place when the materials deform at high temperature. This could directly affect deformation flow, plastic strengthening, the initiation and propagation of microcracks, and finally the fracture failure of materials. In this research, to reveal the high temperature deformation mechanisms of twinning–induced plasticity (TWIP) steels, the crystal plasticity finite element method (CPFEM) was employed to model the mechanical response of grain interiors. The cohesive zone model (CZM) of the bi–linear traction separation law (TSL) was developed to describe the damage and failure of GBs. By combining CZM and CPFEM, an analysis method was proposed to investigate the effect of the microstructure morphology, orientation and size of grains, and temperature. Furthermore, the damage initiation, accumulation and fracture at GBs were represented by the representative volume element model based on the CZM–CPFE method to explore the influences of GB angle, grain size and local microvoids (including the location and size) on the GB cracking. The stress damage cloud maps, the distribution of quadratic stress damage initiation criterion (QUADSCRT) and the scalar stiffness degradation (SDEG) describing the damage and fracture along the GBs were used to articulate the relationships of GB angle, size effect, local microvoids and the expected failure strain. The results show that low angle grain boundaries (LAGBs), the small average grain size (<21.2 μm), microvoids at the horizontal GBs and microvoids with a diameter below 1.5 μm can delay the initiation of microcracks and fracture failure along the GBs. The predicted damage and failure of GBs and the intergranular cracking characteristics in plastic deformation of TWIP steels at high temperature were corroborated by microscopic in–situ SEM experiments, in which the deformation characteristics inside the grains, and microcrack initiation and propagation near GBs were observed at 500 and 750°C. This research enhances the understanding of intergranular fracture, mechanical response and microstructure evolution of TWIP steels worked at different temperatures, and also provides a new way and strategy for studying the deformation behaviours of TWIP steels considering GB properties.

Elastic-plastic progressive damage model and low-velocity impact failure mechanism of composite materials

An elastic-plastic progressive damage model (PDM-3DEP) was proposed to study the mechanical response and damage development of composite laminates under low-velocity impact. The 3D Hashin failure criterion and an improved three-dimensional damage evolution model that considers strain component of ε33 and shear stain are implemented to describe the initiation and evolution of damage modes. The zero-thickness cohesive elements which follow bilinear traction-separation law are applied to simulate delamination. The numerical and experimental mechanical curves and damage distribution of composite laminate with a stacking sequence of 03o/45o/−45oS were compared to verify the proposed PDM-3DEP. The consistent results of the numerical and experimental data indicates that the proposed method can accurately describe damage mechanical behavior under low-velocity impact. Moreover, another type of composite laminate with a stacking sequence of 02o/902o/02o/902o/02oS is adopted for further verification. It is concluded that the proposed model can accurately analyze the mechanical responses of different composite laminates.

Microstructure-sensitive investigation on the mechanical behavior of CNT-reinforced composites considering debonding damage based on cohesive finite element method

In this paper, an analytical modeling and numerical approach based on the finite element (FE) method are introduced to study the influence of the real morphology (e.g., length and waviness) and distribution of carbon nanotubes (CNTs) on the mechanical behavior of the CNT-reinforced composites. The analytical model has considered the real morphology effect using the equivalent curved CNTs with perfect bonding. The equivalent chord length, diameter, and waviness have been computed using the abundance of different values of measured parameters in an actual microstructure of the CNTs in the matrix. In the FE method, a computational tool is used to map an actual composite microstructure onto a FE representative volume element (RVE) with the exact shape, size, distribution, and waviness of CNTs. FE analysis has been carried out in both well-bonded and interface-debonding conditions. The cohesive zone model (CZM) with bilinear traction-separation law for both opening and sliding modes has been utilized to capture the debonding at the CNT-matrix interface. Results indicate that in the presence of weak bonding, CNT waviness can enhance the composite stiffness rather than reduce it. A quite different conclusion to what can be obtained with the assumption of perfect adhesion. In the presence of poor bonding, the curvature has a positive effect on composite properties and improves the load transferring from the matrix. FE analysis for different RVEs highlights that the curvature and length of the CNTs are essential features of the microstructure, and they can effectively influence the mechanical properties of the material. Results demonstrate that the equivalent curved CNTs cannot appropriately represent the real microstructure.

Measurement and FEM of ice adhesion to the downstream pipe of an air cycle machine

Ice accretion on the downstream pipe of an air cycle machine can lead to pipe blockage and turbine blade damage, and therefore de-icing is needed. Most previous studies focused on ice shedding from flat surfaces, and average interface shear strength rather than the true shear strength was usually reported. Here, the debonding of the interface between ice and cylindric surfaces of an aluminium pipe (2024-T3) was studied trying to understand the mechanism of interface fracture and to obtain the true adhesive shear strength and fracture energy. Average adhesive strength was measured first in the scrape test and the result was used to calibrate the finite element analysis. A cohesive zone model (CZM) with bilinear traction-separation law was used to simulate the interface delamination. The true shear strength σcs and mode-II energy release rate Gcs were determined by matching the numerically predicted critical force to the measured force. The influence of shear strength and shear energy release rate on the critical force was also investigated. At the interface, both the damage factor and the peak shear stress were found progressing away from the edge as the pushing force increased. Parametric studies on the influence of the length of the interface was performed. The critical force first increased and then stabilised with the increase of the length, showing the same trend as that of a theoretical model which ignored the mode-I fracture.

Effect of bond-line thickness and mode-mixity on the fracture behavior and traction separation law of Sn-0.7Cu solder joints

In this research, cohesive parameters were extracted for Sn-0.7Cu/Cu solder joint failure. Double cantilever beam (DCB) specimens were used to study the fracture of the joint under both mode-I and mixed-mode conditions. A bilinear traction separation law (TSL) was used to capture the failure of the joint. Increasing the bond-line thickness from 110 to 880 µm increased the critical energy release rate for crack initiation (Gci) and maximum traction of the bilinear TSL. This increase in the Gci was attributed to an increase in plastic zone area (PZA) ahead of the pre-crack tip. Varying the mode-mixity with phase angle (ψ) in the range of 00–330 showed an insignificant change in Gci and maximum traction of the bilinear TSL.

Experimental and numerical investigation of model I dynamic fracture toughness of 95W-3.5Ni-1.5Fe alloy using the semi-circular bend specimens

Semi-circular bend specimens are used to measure the brittle materials' fracture toughness, such as brittle metals, rocks, and ceramic materials. The quasi-static and dynamic model I fracture toughness of tungsten heavy alloy, a typical brittle metal material, are measured using the semi-circular bend specimens under quasi-static compression and dynamic impact loadings. For quasi-static cases, the specimens are loaded on a universal testing machine with a constant loading speed. While for dynamic cases, the specimens are executed on a modified split Hopkinson pressure bar system with the impact pressures from 0.2 to 0.4 MPa. The results show that the dynamic fracture toughness of tungsten alloy increases with the increase of the loading rate. Further, a rate-dependent bilinear traction-separation law is introduced to explain the dynamic fracture behaviors of tungsten alloy. The parameters of the rate-dependent law are obtained from the experiments and the finite element simulations. Finally, the dynamic simi-circular bend simulations using the cohesive element with rate-dependent cohesive law are established to simulate the crack propagation, and the simulation results are in good agreement with the test data.

A hysteresis cohesive approach for predicting mixed-mode delamination onset of composite laminates under cyclic loading: Part I, model development

A new approach is proposed to predict onset of fatigue-induced delamination in composite laminates under cyclic loading by progressive interface degradation. Based on the hysteresis cohesive zone approach, a new damage parameter is defined to construct an irreversible cohesive zone model. Residual displacement jump is introduced and used along with mixed-mode bilinear traction-separation law parameters for calculating the damage parameter. Fatigue-induced delamination onset is then predicted by proposing a damage criterion. 3-D Finite Element (FE) formulation is developed with proper elements for plies and also proper elements for the interface. Cyclic loading is also simulated mimicked by the MIN-MAX method. The current research is conducted in two parts as Part I and Part II. While this article focuses on the theoretical framework of the developed modeling, the numerical implementation of the modeling and also a comparison of the outputs with experimental observations will be presented in the companion paper as Part II.