Micromechanical model for cohesive materials based upon pseudo-granular structure
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Anil Misra↗
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Relevence of 3D Simulations and Sandwich Core Topology for the Modeling of Honeycomb Core Sandwich Panels Undergoing Mode I Delamination
A recently developed cohesive zone traction-separation law, which includes the effects of fiber bridging in a novel way, is extended from 2D to 3D. The proposed cohesive model is applied to low fidelity (i.e. homogenized core representation) and high fidelity (i.e. directly accounting for the core topology) finite element models of a composite panel comprised of carbon fiber reinforced plastic facesheets and a honeycomb sandwich core. This enables the investigation of 2D to 3D parameter transferability, width-dependent effects such as thumbnail-shaped crack growth, and the verification of plane strain / plane stress assumptions. A pronounced curvature of the initial interface-related crack front is observed, while the bridging-related crack front is straight. Furthermore, it is found that the cohesive parameters can easily be transferred from 2D to 3D under plane stress assumptions, but not under plane strain assumptions. The numerical predictions are compared to experimental load-displacement and R-curves.
Composites↗
Quasi-static and Fatigue Delamination at Tape/Fabric Interfaces
The relationship between quasi-static and fatigue delamination of a fabric/tape interface is examined experimentally and numerically.Mixed-mode bending tests were conducted using specimens in which a mid-plane delamination is bound between a ply of 0-degree unidirectional tape and a 0-degree fabric ply of the same material system. The experimental results indicate that delaminations tend to migrate towards the constraining ply that is on the compressive side of the laminate in bending, and that the fracture toughness for a fabric-constrained delamination is almost twice that of a tape-constrained delamination. A cohesive model based on superposition of bilinear laws was used to account for these differences in measured properties. Fatigue analyses were conducted with a cohesive damage model that uses an idealization of stress-life diagrams used in engineering design. The fatigue model is shown to be capable of predicting the steady-state rate of delamination propagation described by the Paris law, as well as the initial transients that depend on the quasi-static R-curve effects. The analysis results help quantify the effects of fracture toughness and R-curves on the rates of delamination propagation in fatigue.
Davila, Carlos G.↗
A Numerical and Experimental Study of Damage Growth in a Composite Laminate
The present study has three goals: (1) perform an experiment where a simple laminate damage process can be characterized in high detail; (2) evaluate the performance of existing commercially available laminate damage simulation tools by modeling the experiment; (3) observe and understand the underlying physics of damage in a composite honeycomb sandwich structure subjected to low-velocity impact. A quasi-static indentation experiment has been devised to provide detailed information about a simple mixed-mode damage growth process. The test specimens consist of an aluminum honeycomb core with a cross-ply laminate facesheet supported on a stiff uniform surface. When the sample is subjected to an indentation load, the honeycomb core provides support to the facesheet resulting in a gradual and stable damage growth process in the skin. This enables real time observation as a matrix crack forms, propagates through a ply, and then causes a delamination. Finite element analyses were conducted in ABAQUS/Explicit(TradeMark) 6.13 that used continuum and cohesive modeling techniques to simulate facesheet damage and a geometric and material nonlinear model to simulate core crushing. The high fidelity of the experimental data allows a detailed investigation and discussion of the accuracy of each numerical modeling approach.
McElroy, Mark↗
TPSAS-NF1676L-19616-DND
The present study has three goals: (1) perform an experiment where a simple laminate damage process can be characterized in high detail; (2) evaluate the performance of existing commercially available laminate damage simulation tools by modeling the experiment; (3) observe and understand the underlying physics of damage in a composite honeycomb sandwich structure subjected to low-velocity impact. A quasi-static indentation experiment has been devised to provide detailed information about a simple mixed-mode damage growth process. The test specimens consist of an aluminum honeycomb core with a cross-ply laminate facesheet supported on a stiff uniform surface. When the sample is subjected to an indentation load, the honeycomb core provides support to the facesheet resulting in a gradual and stable damage growth process in the skin. This enables real time observation as a matrix crack forms, propagates through a ply, and then causes a delamination. Finite element analyses were conducted in ABAQUS/Explicit(TradeMark) 6.13 that used continuum and cohesive modeling techniques to simulate facesheet damage and a geometric and material nonlinear model to simulate core crushing. The high fidelity of the experimental data allows a detailed investigation and discussion of the accuracy of each numerical modeling approach.
Mark McElroy↗
Calculating Mode Mixity in Interlaminar Fracture of Composite Laminates
To accurately predict delamination under mixed-mode loading, cohesive elements must partition the energies dissipated in Mode I and Mode II correctly. The ability of cohesive models to predict mode mixity was evaluated by performing analyses of the single leg bending (SLB) test, which exhibits a variable mode mixity with crack length. Accordingly, two numerical integration methods were developed to compute the energy partitioning: (i) a local calculation of the accumulated work of tractions at each point along the crack path, and (ii) a global J-integral “snapshot” calculation along a contour around the process zone. In the case of a composite laminate with properties characterized by short fracture process zone (FPZ), the results of these two methods correlate well with each other and with a linear elastic fracture mechanics solution. However, FPZscan be long due to fiber bridging or due to the intrinsic toughness of the material. Then, the results of mode-mixity calculations obtained with various methods vary widely from each other. It is argued that the global J-integral calculation is the most accurate interpretation of the energy release rate and mode mixity for either short or long process zones. This solution will provide a more accurate characterization of resistance curves and mode mixity in experimental results, and it will also guide the development of more accurate mixed-mode cohesive laws for tougher materials characterized by strong R-curve responses, such as thermo-plastic composites.
cohesive zone analysis↗
Experimental and Numerical Analysis of Skin-Stiffener Separation Using a Seven-Point Bend Configuration
Skin-stiffener separation in stiffened composite panels consists of a complex interaction between multiple scales of progressive damage and failure mechanisms. This work used a superposed cohesive element method of modeling resistance curve effects that represents the structural interface of a unidirectional tape skin and a fabric stiffener. Finite element models using cohesive elements with input properties obtained from tape-to-fabric interface characterization tests were compared to experimental results of a stable skin-stiffener separation characterization test using a seven-point bend fixture. This fixture deformed the stiffened panel specimens into a buckled configuration which induced mixed-mode interlaminar stress states at the skin-stiffener interface. The advantage of this fixture was the potential for more stable damage initiation and delamination growth compared to a stringer-stiffened panel under axial compression. Use of the superposed cohesive elements showed promise, but the characterization of interface material properties as input to the cohesive elements remains a crucial component to be investigated to ensure accurate prediction of skin-stiffener separation.
Kosztowny, Cyrus J. R.↗
Molecular-dynamics Simulation-based Cohesive Zone Representation of Intergranular Fracture Processes in Aluminum
A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics simulations. A molecular-dynamics model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat 99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two opposite directions along the grain boundary. In one direction, the crack propagates in a brittle manner by cleavage with very little or no dislocation emission, and in the other direction, the propagation is ductile through the mechanism of deformation twinning. This behavior is consistent with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion. A comparison with finite element calculations shows that while the stress field around the brittle crack tip follows the expected elastic solution for the given boundary conditions of the model, the stress field around the twinning crack tip has a strong plastic contribution. Through the definition of a Cohesive-Zone-Volume-Element an atomistic analog to a continuum cohesive zone model element - the results from the molecular-dynamics simulation are recast to obtain an average continuum traction-displacement relationship to represent cohesive zone interaction along a characteristic length of the grain boundary interface for the cases of ductile and brittle decohesion. Keywords: Crack-tip plasticity; Cohesive zone model; Grain boundary decohesion; Intergranular fracture; Molecular-dynamics simulation
Yamakov, Vesselin I.↗
Durability and life prediction modeling in polyimide composites
Sudden appearance of cracks on a macroscopically smooth surface of brittle materials due to cooling or drying shrinkage is a phenomenon related to many engineering problems. Although conventional strength theories can be used to predict the necessary condition for crack appearance, they are unable to predict crack spacing and depth. On the other hand, fracture mechanics theory can only study the behavior of existing cracks. The theory of crack initiation can be summarized into three conditions, which is a combination of a strength criterion and laws of energy conservation, the average crack spacing and depth can thus be determined. The problem of crack initiation from the surface of an elastic half plane is solved and compares quite well with available experimental evidence. The theory of crack initiation is also applied to concrete pavements. The influence of cracking is modeled by the additional compliance according to Okamura's method. The theoretical prediction by this structural mechanics type of model correlates very well with the field observation. The model may serve as a theoretical foundation for future pavement joint design. The initiation of interactive cracks of quasi-brittle material is studied based on a theory of cohesive crack model. These cracks may grow simultaneously, or some of them may close during certain stages. The concept of crack unloading of cohesive crack model is proposed. The critical behavior (crack bifurcation, maximum loads) of the cohesive crack model are characterized by rate equations. The post-critical behavior of crack initiation is also studied.
Binienda, Wieslaw K.↗
Continuum Damage Mechanics Models for the Analysis of Progressive Failure in Open-Hole Tension Laminates
The performance of a state-of-the-art continuum damage mechanics model for interlaminar damage, coupled with a cohesive zone model for delamination is examined for failure prediction of quasi-isotropic open-hole tension laminates. Limitations of continuum representations of intra-ply damage and the effect of mesh orientation on the analysis predictions are discussed. It is shown that accurate prediction of matrix crack paths and stress redistribution after cracking requires a mesh aligned with the fiber orientation. Based on these results, an aligned mesh is proposed for analysis of the open-hole tension specimens consisting of different meshes within the individual plies, such that the element edges are aligned with the ply fiber direction. The modeling approach is assessed by comparison of analysis predictions to experimental data for specimen configurations in which failure is dominated by complex interactions between matrix cracks and delaminations. It is shown that the different failure mechanisms observed in the tests are well predicted. In addition, the modeling approach is demonstrated to predict proper trends in the effect of scaling on strength and failure mechanisms of quasi-isotropic open-hole tension laminates.
Song, Kyonchan↗
Analysis of Progressive Damage in Cross-Ply and Quasi-Isotropic Panels Subjected to Quasi-Static Indentation
The performance of a three-dimensional continuum damage mechanics (CDM) model for intralaminar damage, coupled with a cohesive zone model for delamination, is examined for damage prediction in cross-ply and quasi-isotropic laminated plates subjected to quasi-static transverse indentation. Details of the CDM model based on the deformation gradient decomposition (DGD) method and the finite element (FE) modeling strategy are presented and discussed. Critical features of the damage model and FE modeling approach are assessed by comparing analysis predictions to experimental data for cross-ply and quasi-isotropic panels in which damage is dominated by complex interactions between matrix cracks and delaminations.
Song, Kyongchan↗
Development of a Combined Cohesive and Virtual Crack-Closure Technique Approach to Represent R-Curves
Resistance curve (R-curve) effects due to fiber bridging, crack migration, and other blunting mechanisms are common in composite laminates. These mechanisms can dramatically increase the resistance to crack propagation but can be challenging to simulate. Delamination with R-curves can be analyzed using cohesive zone modeling (CZM) or the virtual crack closure technique (VCCT). Large fracture process zones can be simulated with CZM, but they require highly refined meshes. Coarser meshes can be used with VCCT, but this method is only applicable to small fracture process zones with R-curves defined as functions of position. Therefore, a technique with the computational efficiency of VCCT and the natural ability of cohesive elements to represent large fracture process zones is desirable. An approach is proposed that starts as a CZM in which the cohesive traction separation law (TSL) is separated into high-strength (HS) and low-strength (LS) components. The HS part, which is responsible for the mesh requirements of the CZM analysis, is replaced by VCCT. The combined method is evaluated by analyzing the response of double cantilevered beam specimens. Two specimen layup configurations, [0/90/90/0] 3s and [0/90/90/0] 9s , are evaluated. The R-curve response from each configuration is determined and applied to the constitutive properties of models built with CZM and with VCCT. The results and computational efficiency of the CZM, VCCT, and combined approaches are compared. The results are indicative that a combined cohesive/VCCT approach can enable progressive failure analyses to retain the computational efficiency of VCCT with the ability of the cohesive elements to capture R-curve effects.
Virtual Crack-Closure Technique↗
Stress Distribution During Deformation of Polycrystalline Aluminum by Molecular-Dynamics and Finite-Element Modeling
In this paper, a multiscale modelling strategy is used to study the effect of grain-boundary sliding on stress localization in a polycrystalline microstructure with an uneven distribution of grain size. The development of the molecular dynamics (MD) analysis used to interrogate idealized grain microstructures with various types of grain boundaries and the multiscale modelling strategies for modelling large systems of grains is discussed. Both molecular-dynamics and finite-element (FE) simulations for idealized polycrystalline models of identical geometry are presented with the purpose of demonstrating the effectiveness of the adapted finite-element method using cohesive zone models to reproduce grain-boundary sliding and its effect on the stress distribution in a polycrystalline metal. The yield properties of the grain-boundary interface, used in the FE simulations, are extracted from a MD simulation on a bicrystal. The models allow for the study of the load transfer between adjacent grains of very different size through grain-boundary sliding during deformation. A large-scale FE simulation of 100 grains of a typical microstructure is then presented to reveal that the stress distribution due to grain-boundary sliding during uniform tensile strain can lead to stress localization of two to three times the background stress, thus suggesting a significant effect on the failure properties of the metal.
Yamakov, V.↗
Overview of Coupon Testing of an IM7/8552 Composite Required to Characterize High-Energy Impact Dynamic Material Models
As part of NASA’s Advanced Composites Project (ACP), a significant research effort was established to develop and mature analysis methods for composite materials particularly applicable to high-energy dynamic impact applications. An overall goal was to develop and advance analysis methods that can be characterized using fundamental coupon level tests. Based on this fundamental characterization, simulations at the higher levels of a building block approach can be purely predictive. The tests described in this report were performed on a unidirectional carbon fiber polymer matrix composite, IM7/8552 tape, as this material system is representative of a modern aerospace grade carbon fiber tape system. These tests were chosen to provide fundamental material characterization data for three representative progressive damage and failure analysis material models available within the LS-DYNA commercial transient dynamic finite element code for use in the simulation of the dynamic and impact response of composite materials. Two of the material models, MAT162 and MAT261, are well established material models within LS-DYNA. The third material model, MAT213, is under active development. Testing consisted primarily of ASTM-type standard tests, and the tests that were performed were consistent with the needs of all three models. Additionally, coupon level tests were performed that can be used to characterize a delamination model (e.g., cohesive zone or tie-break contact). While, the tests described in this report provide fundamental material characterization data for all three of the material models mentioned above, the data is applicable to additional material models not discussed.
Justusson, Brian P.↗
TPSAS-NF1676L-32227-DND
The ability of a recently proposed cohesive fatigue model to predict the initiation and propagation of skin/stiffener separation was evaluated using a three-point bend (3PB) configuration. The 3PB specimen consists of a quasi-isotropic laminate representing the skin of a fuselage. A shorter doubler representing the flange of a stiffener is co-cured at the center of the specimen. A simplified modeling technique was applied, in which the complex damage mechanisms involved in the separation, such as delamination migration, matrix cracking, bridging, and crack delving are represented by a mixed-mode trilinear cohesive law at the interface between the skin and the doubler. The quasi-static properties of the trilinear law were characterized. The main advantage of the proposed fatigue model is that it relies on quasi-static properties as well as engineering assumptions to compose the shape of the S-N diagram. The model does not require Paris law data, and it is capable of predicting the initiation of separation, the rate of propagation, as well as the effects of crack resistance curves and the stress ratio.
Carlos G Davila↗
Delamination Modeling of Composites for Improved Crash Analysis
Finite element crash modeling of composite structures is limited by the inability of current commercial crash codes to accurately model delamination growth. Efforts are made to implement and assess delamination modeling techniques using a current finite element crash code, MSC/DYTRAN. Three methods are evaluated, including a straightforward method based on monitoring forces in elements or constraints representing an interface; a cohesive fracture model proposed in the literature; and the virtual crack closure technique commonly used in fracture mechanics. Results are compared with dynamic double cantilever beam test data from the literature. Examples show that it is possible to accurately model delamination propagation in this case. However, the computational demands required for accurate solution are great and reliable property data may not be available to support general crash modeling efforts. Additional examples are modeled including an impact-loaded beam, damage initiation in laminated crushing specimens, and a scaled aircraft subfloor structures in which composite sandwich structures are used as energy-absorbing elements. These examples illustrate some of the difficulties in modeling delamination as part of a finite element crash analysis.
Fleming, David C.↗
Delamination Modeling of Composites for Improved Crash Analysis
Finite element crash modeling of composite structures is limited by the inability of current commercial crash codes to accurately model delamination growth. Efforts are made to implement and assess delamination modeling techniques using a current finite element crash code, MSC/DYTRAN. Three methods are evaluated, including a straightforward method based on monitoring forces in elements or constraints representing an interface; a cohesive fracture model proposed in the literature; and the virtual crack closure technique commonly used in fracture mechanics. Results are compared with dynamic double cantilever beam test data from the literature. Examples show that it is possible to accurately model delamination propagation in this case. However, the computational demands required for accurate solution are great and reliable property data may not be available to support general crash modeling efforts. Additional examples are modeled including an impact-loaded beam, damage initiation in laminated crushing specimens, and a scaled aircraft subfloor structures in which composite sandwich structures are used as energy-absorbing elements. These examples illustrate some of the difficulties in modeling delamination as part of a finite element crash analysis.
Fleming, David C.↗
Progressive Failure Analysis Correlation with Notched Composite Laminate Test Data
Testing of small and intermediate laminate panels with notches was performed and Progressive Failure Analyses (PFA) models were developed for aid in test planning and for correlation with the test data. Two progressive damage failure models were included in the study: the commercially available Abaqus built-in damage model and COmplete STress Reduction (COSTR) damage model developed at NASA Langley Research Center (LaRC). The finite elements models used for the analysis were developed using shell elements. The pre-test PFA results obtained from the two damage models were compared to test data. Then a post-test PFA with updated material properties based on additional available material property data was executed with the COSTR damage model and compared to the test data. The panels tested in compression all exhibited less scatter in the failure load with self-similar failure behavior. The panels tested in tension exhibited more scatter in the failure load with a failure mode that included delamination of plies. However, a self-similar crack path was also observed as the overall failure mode for all panels tested. When comparing test data to the pre-test analysis results, both damage models with shell element models were considered adequate for predicting the behavior and failure load of both the small and intermediate panels when tested in compression. However, for the tension load cases, larger differences were observed between the test and analysis results. When comparing test data to the post-test analysis performed using the COSTR damage model, better correlation was observed. However, large discrepancies were still observed for the tension load cases. Consequently, a higher fidelity finite element model including solid elements for sub-laminates and the modeling of cohesive layers between sub-laminate layers is recommended for tension loading of notched composite laminates.
Damage Model,Progressive Failure Analysis,Open Hol↗