A level set model for simulating fatigue-driven delamination in composites

This paper proposes a level set model for simulating delamination propagation in composites under high-cycle fatigue loading. For quasi-static loading conditions, interface elements with a cohesive law are widely used for the simulation of delamination. However, basic concepts from fatigue analysis such as the notion that the crack growth rate is a function of energy release rate cannot be embedded in existing cohesive laws. Therefore, we propose a model in which the cohesive zone is eliminated from the computation while maintaining the flexibility that the crack shape is not bound to element edges. The model is able to predict the delamination growth rate and its front shape accurately. To demonstrate the validity of the model, several tests under different fracture modes are conducted and the results are compared with experimental data, analytical solutions and results from cohesive zone analysis.     

Integrated XFEM-CE analysis of delamination migration in multi-directional composite laminates

Progressive damage and failure in composites are generally complex and involve multiple interacting failure modes. Depending on factors such as lay-up sequence, loading and specimen configurations, failure may be dominated by extensive matrix crack-delamination interactions, which are very difficult to model accurately. The present study further develops an integrated extended finite element method (XFEM) and cohesive element (CE) method for three-dimensional (3D) delamination migration in multi-directional composite laminates, and validates the results with experiment performed on a double-cantilever beam (DCB). The plies are modeled by using XFEM brick elements, while the interfaces are modeled using CEs. The interaction between matrix crack and delamination is achieved by enriching the nodes of cohesive element. The mechanisms of matrix fracture and delamination migration are explained and discussed. Matrix crack initiation and propagation can be predicted and delamination migration is also observed in the results. The algorithm provides for the prediction of matrix crack angles through the ply thickness. The proposed method provides a platform for the realistic simulation of progressive failure of composite laminates.     

Bilinear approximations to the mode II delamination cohesive law using an inverse method

Cohesive zone modelling has proved to be a powerful tool to model delamination problems in high performance composites. Application to mode II delamination is of particular interest due to the large fracture process zone. In this paper, bilinear approximations to the mode II delamination cohesive law were determined for two carbon/epoxy composites. This was achieved by an inverse method that consisted of making Finite Element Analyses fit experimental load–displacement curves measured in well-known End-Notched Flexure tests. The optimal parameters of the bilinear cohesive law were determined by a genetic algorithm. The results showed the adequacy of the bilinear cohesive law and of the methodology employed.     

A Cohesive Zone Approach for Fatigue-Driven Delamination Analysis in Composite Materials

A new model for prediction of fatigue-driven delamination in laminated composites is proposed using cohesive interface elements. The presented model provides a link between cohesive elements damage evolution rate and crack growth rate of Paris law. This is beneficial since no additional material parameters are required and the well-known Paris law constants are used. The link between the cohesive zone method and fracture mechanics is achieved without use of effective length which has led to more accurate results. The problem of unknown failure path in calculation of the energy release rate is solved by imposing a condition on the damage model which leads to completely vertical failure path. A global measure of energy release rate is used for the whole cohesive zone which is computationally more efficient compared to previous similar models. The performance of the proposed model is investigated by simulation of well-known delamination tests and comparison against experimental data of the literature.     

Overcoming the cohesive zone limit in composites delamination: modeling with slender structural elements and higher-order adaptive integration

Cohesive element (CE) is a well-established finite element for fracture, widely used for the modeling of delamination in composites. However, an extremely fine mesh is usually needed to resolve the cohesive zone, making CE-based delamination analysis computationally prohibitive for applications beyond the scale of lab coupons. In this work, a new CE-based method of modeling delamination in composites is proposed to overcome this cohesive zone limit on the mesh density. The proposed method makes use of slender structural elements for the plies, a compatible formulation with adaptive higher-order integration for the CEs, and the corotational formulation for geometrically nonlinear analysis. The proposed method is verified and validated on the classical benchmark problems of Mode I, II, mixed-mode delamination, a buckling-induced delamination problem and a double-delamination problem. The results show that elements much larger than the cohesive zone length can be used while retaining accuracy.     

Numerical analysis of size effects on open-hole tensile composite laminates

The tensile strength of open-hole fibre reinforced composite laminates depends on in-plane, thickness and ply lay-up scaling. Translaminar (fibre direction) mode I fracture toughness has recently been experimentally determined to be thickness dependent. This paper presents a computational study of the tensile strength prediction of open-hole laminates using a cohesive zone model. To the authors’ knowledge, it is for the first time in the literature that the thickness-dependence of translaminar fracture toughness is accounted for in the numerical modelling of composites. The thickness size effect in the strength of open-hole composite laminates failed by pull-out is accurately predicted for the first time by a deterministic model. It is found that neglecting delamination in the numerical models will lead to mesh-dependency and over-estimation on the predicted strength. Smeared crack model with cohesive elements to model delamination is able to predict the correct failure mode; but it is found not suitable for accurate strength predictions for laminates failed by delamination.     

Predicting mode-II delamination suppression in z-pinned laminates

A finite element model for predicting delamination resistance of z-pin reinforced laminates under the mode-II load condition is presented. End notched flexure specimen is simulated using a cohesive zone model. The main difference of this approach to previously published cohesive zone models is that the individual bridging force exerted by z-pin is governed by a specific traction-separation law derived from a unit-cell model of single pin failure process, which is independent of the fracture toughness of the unreinforced laminate. Therefore, two separate traction-separation laws are employed; one represents unreinforced laminate properties and the other for the enhanced delamination toughness owing to the pin bridging action. This approach can account for the so-called large scale bridging effect and avoid using concentrated pin forces in numerical models, thus removing the mesh-size dependency and permitting more accurate and reliable computational solutions.     

Delamination buckling and propagation analysis of honeycomb panels using a cohesive element approach

The cohesive element approach is proposed as a tool for simulating delamination propagation between a facesheet and a core in a honeycomb core composite panel. To determine the critical energy release rate (G _c) of the cohesive model, Double Cantilever Beam (DCB) fracture tests were performed. The peak strength (_c) of the cohesive model was determined from Flatwise Tension (FWT) tests. The DCB coupon test was simulated using the measured fracture parameters, and sensitivity studies on the parameters for the cohesive model of the interface element were performed. The cohesive model determined from DCB tests was then applied to a full-scale, 914×914 mm (36×36 in.) debond panel under edge compression loading, and results were compared with an experiment. It is concluded that the cohesive element approach can predict delamination propagation of a honeycomb panel with reasonable accuracy.     

Cohesive modeling of delamination in Z-pin reinforced composite laminates

The mode I interlaminar fracture in Z-pin reinforced composite laminates is modeled using a cohesive volumetric finite element (CVFE) scheme. The test configuration used in this study is a Z-pin reinforced double cantilever beam specimen. A bilinear rate-independent but damage-dependent cohesive traction–separation law is adopted to model the fracture of the unreinforced composite and discrete nonlinear spring elements to represent the effect of the Z-pins. The delamination toughness and failure strength of the Z-pin reinforced composites are determined by a detailed comparison study of the numerical modeling results with experimental data. To further reduce the computational effort, we introduce an equivalent distributed cohesive model as a substitute for the discrete nonlinear spring representation of the Z-pins. The cohesive model is implemented on various test problems with varying failure parameters and for varying spatial Z-pin reinforcement configurations showing good agreement with the experimental results.     

基于界面断裂的粘聚区长度计算方法研究

基于各向异性双材料界面断裂力学理论,再根据D-B模型假设的有限裂纹尖端奇异性将消失,推导出复合材料分层裂纹尖端粘聚区长度的计算模型。结果显示复合材料分层裂纹尖端粘聚区具有振荡性(当振荡因子0时),并且粘聚区长度与裂纹长度、应力值及振荡因子有关。将新模型应用于界面单元法中,模拟了双悬臂梁(DCB)和混合型弯曲梁(MBB)分层扩展过程中的载荷-位移关系,并比较了不同的粘聚区长度对收敛性和计算精度的影响,结果表明该模型可较精确地计算复合材料的粘聚区长度,以此为基础划分网格能同时保证收敛性和计算精度要求,并可有效地节省运算时间。     

Influence of temperature on the delamination process under mode I fracture and dynamic loading of two carbon–epoxy composites

This paper experimentally analyzes the influence of temperature and type of matrix on the delamination process of two composites subjected to fatigue loading through the study of their fracture under mode I behavior. The materials were manufactured with the same AS4 unidirectional carbon reinforcement and two epoxy matrices with different fracture behavior. The chosen temperatures for the experiments were 20 (room temperature), 50 and 90 °C.The experimental study carried out under dynamic loading enabled the authors to determine the influence that temperature has on the onset of delamination for the entire range of fatigue life of the material, from the low number of cycles zone to the high number of cycles zone. That is, it enabled the plotting of fatigue curves, represented as G_Imax–N (number of cycles required for the onset of delamination given a certain energy release rate) for an asymmetry coefficient of 0.2 (the ratio between the maximum and minimum fracture energies applied during the dynamic tests).The experimental data obtained were treated with a probabilistic model based on a Weibull distribution which allowed the identification of relevant aspects of the fatigue behavior of the materials such as the estimation of fatigue strength for periods greater than the tested values and the analysis of the reliability of the results.     

Modeling progressive delamination of laminated composites by discrete element method

Discrete element method (DEM) was used to model progressive delamination of fiber reinforced composite laminates. The anisotropic composite plies were constructed through a hexagonal packing of particle elements. Contacts between the particles were represented by parallel bonds with the verified normal and shear elastic properties. The ply interface was characterized by a contact softening model with a bilinear elastic behavior which is similar to the cohesive zone model in the continuum mechanics. DCB, ELS and FRMM tests were simulated by the DEM model to assess its capability of modeling mode I, mode II and mix mode fracture of delamination, respectively. Good agreements were observed between the DEM and existing numerical and experimental results of loading curves, which confirmed that the DEM model can be used to simulate initiation and propagation of composite delamination, with more insights into microscopic material behavior, such as damage extension and plastic zone.     

Simulation of delamination by means of cohesive elements using an explicit finite element code

This paper presents the formulation of a tri-dimensional cohesive element implemented in a user-written material subroutine for explicit finite element analysis. The cohesive element simulates the onset and propagation of the delamination in advanced composite materials. The delamination model is formulated by using a rigorous thermodynamic framework which takes into account the changes of mixed-mode loading conditions. The model is validated by comparing the finite element predictions with experimental data obtained in interlaminar fracture tests under quasi-static loading conditions.     

Energy absorption and damage propagation in 2D triaxially braided carbon fiber composites: effects of in situ matrix properties

Results from an experimental program to investigate the propagation of damage and energy dissipation in 2D triaxially braided carbon fiber textile composites (2DTBC) under static conditions are reported. A methodology is presented in which classical concepts from fracture mechanics are generalized to address damage growth in an orthotropic and heterogeneous structural material. Along with results from the experimental program, a novel numerical technique that employs ideas from cohesive zone modeling, and implemented through the use of finite-element analysis, is also presented. The inputs that are required for the discrete cohesive zone model (DCZM) are identified. Compact tension specimen fracture tests and double notched tension tests were carried out to measure the fracture energy (G _Ic), and the maximum cohesive strength (σ _c), of the 2DTBC. The DCZM modeling strategy was independently verified by conducting single edge notched three-point bend tests using a modified three-point bend test fixture. The experimental and numerical analyses were carried out for two different types of 2DTBC made from the same textile architecture but infused with two different resin systems to validate the proposed methodology.     

Experimental and numerical analysis on Mode-I delamination of CFRP laminates toughened by polyamide non-woven fabric layer

The objective of this research is to put forward a toughening method by using the polyamide non-woven fabric (PNF) and investigate the Mode-I fracture toughness and delamination characteristic of the toughened CFRP laminates by performing the double cantilever beam test. The effect of PNF interlayer, which is formulated by a bilinear cohesive zone model, on the Mode-I fracture of U3160-PNF/3266 laminated composites is numerically analyzed. And the intralaminar damages are considered by using strength criteria and stiffness degradation law. The influences of PNF/3266 interlayer strength, U3160/3266 laminate thickness and initial crack length on the mechanical response of laminates are studied systematically. The work by combining the experiment and simulation is helpful for the optimal design of laminated composites used in aerospace and civil engineering.     

Finite element model for compression after impact behaviour of stitched composites

A finite element (FE) model using coupling continuum shell elements and cohesive elements is proposed to simulate the compression after impact (CAI) behaviour and predict the CAI strength of stitched composites. Continuum shell elements with Hashin failure criterion exhibit the composite laminate damage behaviour; whilst cohesive elements using traction-separation law characterise the laminate interfaces. Impact-induced delamination is explicitly modelled by reducing material properties of damaged cohesive elements. Computational results have demonstrated the trend of increasing CAI strength with decreasing impact-induced delamination area. Spring elements are introduced into the model to represent through-thickness stitch thread in the composite laminates. Results in this study validate experimental finding that CAI strength is improved when stitching is incorporated into the composite structure. The proposed FE model reveals good CAI strength predictions and indicates good agreement with experimental results, making it a valuable tool for CAI strength prediction of stitched composites.     

Predicting crack propagation with peridynamics: a comparative study

The fidelity of the peridynamic theory in predicting fracture is investigated through a comparative study. Peridynamic predictions for fracture propagation paths and speeds are compared against various experimental observations. Furthermore, these predictions are compared to the previous predictions from extended finite elements (XFEM) and the cohesive zone model (CZM). Three different fracture experiments are modeled using peridynamics: two experimental benchmark dynamic fracture problems and one experimental crack growth study involving the impact of a matrix plate with a stiff embedded inclusion. In all cases, it is found that the peridynamic simulations capture fracture paths, including branching and microbranching that are in agreement with experimental observations. Crack speeds computed from the peridynamic simulation are on the same order as those of XFEM and CZM simulations. It is concluded that the peridynamic theory is a suitable analysis method for dynamic fracture problems involving multiple cracks with complex branching patterns.     

Crack growth resistance behavior of a functionally graded material: computational studies

This paper describes crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) using a cohesive zone ahead of the crack front. The plasticity in the background (bulk) material follows J₂ flow theory with the flow properties determined by a volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model). A phenomenological, cohesive zone model with six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) describes the constitutive response of the cohesive zone. Crack growth occurs when the complete separation of the cohesive surfaces takes place. The crack growth resistance of the FGM is characterized by a rising J-integral with crack extension (averaged over the specimen thickness) computed using a domain integral (DI) formulation. The 3-D analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. The paper describes applications of the cohesive zone model and the DI method to compute the J resistance curves for both single-edge notch bend, SE(B), and single-edge notch tension, SE(T), specimens having properties of a TiB/Ti FGM. The numerical results show that the TiB/Ti FGM exhibits significant crack growth resistance behavior when the crack grows from the ceramic-rich region into the metal-rich region. Under these conditions, the J-integral is generally higher than the cohesive energy density at the crack tip even when the background material response remains linearly elastic, which contrasts with the case for homogeneous materials wherein the J-integral equals the cohesive energy density for a quasi-statically growing crack.     

A consistent partly cracked XFEM element for cohesive crack growth

Present extended finite element method (XFEM) elements for cohesive crack growth may often not be able to model equal stresses on both sides of the discontinuity when acting as a crack‐tip element. The authors have developed a new partly cracked XFEM element for cohesive crack growth with extra enrichments to the cracked elements. The extra enrichments are element side local and were developed by superposition of the standard nodal shape functions for the element and standard nodal shape functions for a sub‐triangle of the cracked element. With the extra enrichments, the crack‐tip element becomes capable of modelling variations in the discontinuous displacement field on both sides of the crack and hence also capable of modelling the case where equal stresses are present on each side of the crack. The enrichment was implemented for the 3‐node constant strain triangle (CST) and a standard algorithm was used to solve the non‐linear equations. The performance of the element is illustrated by modelling fracture mechanical benchmark tests. Investigations were carried out on the performance of the element for different crack lengths within one element. The results are compared with previously obtained XFEM results applying fully cracked XFEM elements, with computational results achieved using standard cohesive interface elements in a commercial code, and with experimental results. The suggested element performed well in the tests. Copyright © 2007 John Wiley & Sons, Ltd.