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In carrying out fatigue delamination propagation tests to assess the propagation rate versus a function of the energy release rate, the question arises as to the necessary number of cycles required to properly characterize the behavior. Tests were performed elsewhere on two different carbon/epoxy, multidirectional woven composite laminates containing a delamination using constant amplitude cycling by means of displacement control for various cycle ratios. The aim was to carry out the tests for 3.0×106 cycles. Most specimens complied with this requirement. In this study, the fatigue data are analyzed including the first 0.5×106 cycles, the first 1.0×106 cycles, the first 1.5×106 cycles, and 3.0×106 cycles. It was seen that although the delamination length versus the cycle number could be quite similar between different cycle ranges, the Paris relation constants could be significantly different. It is suggested to carry out tests for as many cycles as possible. Highlights: Double cantilever beam (DCB) specimens fabricated from multidirectional woven material were considered.Two material systems were examined.Different cycle ranges were used: 0.5 × 106, 1.0 × 106, 1.5 × 106, and 3.0 × 106.It was found that more reliable results were obtained for longer cycle ranges. [ABSTRACT FROM AUTHOR]

Fatigue delamination damage is one of the most important fatigue failure modes for laminated composite structures. However, there are still many challenging problems in the development of the theoretical framework, mathematical/physical models, and numerical simulation of fatigue delamination. What is more, it is essential to establish a systematic classification of these methods and models. This article reviews the experimental phenomena of delamination onset and propagation under fatigue loading. The authors reviewed the commonly used phenomenological models for laminated composite structures. The research methods, general modeling formulas, and development prospects of phenomenological models were presented in detail. Based on the analysis of finite element models (FEMs) for laminated composite structures, several simulation methods for fatigue delamination damage models (FDDMs) were carefully classified. Then, the whole procedure, range of applications, capability assessment, and advantages and limitations of the models, which were based on four types of theoretical frameworks, were also discussed in detail. The theoretical frameworks include the strength theory model (SM), fracture mechanics model (FM), damage mechanics model (DM), and hybrid model (HM). To the best of the authors' knowledge, the FDDM based on the modified Paris law within the framework of hybrid fracture and damage mechanics is the most effective method so far. However, it is difficult for the traditional FDDM to solve the problem of the spatial delamination of complex structures. In addition, the balance between the cost of acquiring the model and the computational efficiency of the model is also critical. Therefore, several potential research directions, such as the extended finite element method (XFEM), isogeometric analysis (IGA), phase-field model (PFM), artificial intelligence algorithm, and higher-order deformation theory (HODT), have been presented in the conclusions. Through validation by investigators, these research directions have the ability to overcome the challenging technical issues in the fatigue delamination prediction of laminated composite structures. [ABSTRACT FROM AUTHOR]

In this paper, the application requirement of the Residual Property Model based on the decrescent exponential function is reduced to only one mechanical test datum. For this, by using Creager and Paris's elastic stress field equation in front of the blunt elliptical hole, the theoretical radius was chosen for the tip curvative and the maximum stress in the load direction at the tip is ensured to be equal the fracture toughness. Thus, the workload of the model is reduced by making the u exponent in the e-u function dependent on the geometric correction factor and the crack length. It was applied to the laminated composite specimens with three-point bending and the specimens including circular hole, and critical fracture stress values close to actual values were achieved. [ABSTRACT FROM AUTHOR]

The transverse cracking behavior of a carbon-fiber-reinforced plastic (CFRP) cross-ply laminate is investigated using a fatigue test and an entropy-based failure criterion in this study. The results of fatigue experiments show that the crack accumulation behavior depends on the cyclic number level and frequency, in which two obvious transverse cracks are observed after 104 cyclic loads and 37 transverse cracks occur after 105 cycles. The final numbers of transverse cracks decrease from 29 to 11 when the load frequency increases from 5 Hz to 10 Hz. An entropy-based failure criterion is proposed to predict the long-term lifetime of laminates under cyclic loadings. The transverse strength of 90° ply is approximated by the Weibull distribution for a realistic simulation. Progressive damage and transverse cracking behavior in CFRP ply can be reproduced due to entropy generation and strength degradation. The effects of stress level and load frequency on the transverse cracking behavior are investigated. It is discovered that, at the edge, the stress σ22 + σ33 that is a dominant factor for matrix tensile failure mode is greater than the interior at the first cycle load, and as stress levels rise, a transverse initial crack forms sooner. However, the initial transverse crack initiation is delayed as load frequencies increase. In addition, transverse crack density increases quickly after initial crack formation and then increases slowly with the number of load cycles. The proposed method's results agree well with those of the existing experimental method qualitatively. In addition, the proposed entropy-based failure criterion can account for the effect of load frequency on transverse crack growth rate, which cannot be addressed by the well-known Paris law. [ABSTRACT FROM AUTHOR]

Fatigue/fracture characterization of carbon-epoxy laminates under pure mode I loading is addressed in this work. Double cantilever beam fatigue/fracture tests were performed to obtain the fatigue lives and the modified Paris law parameters representative of stable crack growth. These experimental Paris law coefficients were used as input parameters in a high-cycle fatigue cohesive zone model. The fatigue life obtained in the numerical simulation was compared with the experimental ones and a good agreement between them was found. Subsequently, the numerical model was used to evaluate the influence of several parameters on the mode I interlaminar fatigue/fracture behavior of CFRP laminates. [ABSTRACT FROM AUTHOR]

In this paper, a numerical tool, able to mimic the delamination growth under cyclic loading conditions, has been adopted to investigate the mode II interlaminar damage growth in composite laminates. An improved Virtual Crack Closure Technique based model, mesh and time step independent, has been combined with a Paris‐Law equations‐based model to account for the effects of cycling loading conditions on the structural behavior of a specimen under an End‐Notched Flexure (ENF) test. The ANSYS FEM environment has been adopted for the numerical simulations and the numerical model has been implemented in ANSYS by adopting the Ansys Parametric Design Language (APDL). Comparisons at the coupon level with literature experimental data on unidirectional ENF samples have demonstrated the ability of the numerical model to simulate the Mode II fatigue delamination growth. Actually, useful indications on the damage propagation under fatigue loading condition have been provided by the proposed numerical model in conjunction with the experimental data taken from literature. [ABSTRACT FROM AUTHOR]

A modeling approach is proposed to simulate delamination propagation in composite laminates under both quasi-static and fatigue loading regimes. Delamination growth is simulated using the Virtual Crack Closure Technique combined with a progressive nodal release strategy. In the proposed approach, the delamination propagation increment is determined explicitly, based on the energy release rate calculated in the previous time increment. Explicitly determining the delamination propagation increment linearizes the system of equations that results from the progressive nodal release strategy and eliminates convergence issues associated with delamination growth. In fatigue, the delamination growth increment is calculated using as input growth rates characterized experimentally via fitting of a suitable form of the Paris law to the experimental data. Under quasi-static loading conditions, a sufficiently large pseudo-growth rate is assumed, such that the simulation results converge to the results obtained with the chosen binary (growth/no growth) fracture criterion. Since both fatigue and quasi-static loading regimes share the same underlying algorithm, simulating the transition between fatigue and quasi-static delamination growth is trivial. The approach is demonstrated to accurately simulate delamination growth for all cases assessed, including quasi-static mixed-mode loading and the transition between fatigue and quasi-static delamination growth regimes. Finally, it is also shown that the approach can simulate both self-similar and non-self-similar delamination growth. [ABSTRACT FROM AUTHOR]

• A novel damage model for matrix crack damage under fatigue loading is proposed based on damage mechanics at macro level. • The damage model takes into account the 'edge effect' of matrix cracks in composite laminate under fatigue loading. • The model is applicable to laminated composites under fatigue loading with different stress levels. • Experimental validation demonstrated the effectiveness and predictive capability of the model. A damage model for transverse matrix cracks in composite laminates under fatigue loading was presented in this paper. The model was prosed based on the theory of continuum damage mechanics (CDM) at macro level and could capture the 'edge effect' of matrix cracks in composite laminate under fatigue loading. To obtain the constitutive equation of UD lamina containing transverse matrix cracks, a polynomial Gibbs free energy function was derived, and a macro damage parameter was introduced to characterize the influence of matrix cracks on multidirectional stiffness properties of UD composite. To predict the initiation and evolution of matrix cracks, a previously deduced initial crack initiation life function and a Paris-like equation in terms of damage driving force were employed, respectively. Prediction results of two cross-ply laminates under fatigue loading with different stress levels were compared to the experimental results and prediction results obtained from previously proposed model. The comparison results indicate the presented model is more effective and reliable in predicting the initiation and evolution of matrix cracks and the corresponding stiffness degradation in composite laminates under fatigue loading. [ABSTRACT FROM AUTHOR]

With the recent demand for weight reduction, structural materials for transportation equipment are being replaced by carbon-fiber-reinforced thermoplastics (CFRTPs). Therefore, techniques to join CFRTPs to alloys are needed. In this study, the fatigue delamination growth of bonded CFRTP/aluminum alloy joints was characterized. The specimens were bonded in three ways, using adhesive, direct chemical bonding, and direct chemical bonding with a nanostructured surface. The type of the specimen was double cantilever beam (DCB) specimen, which consisted of aluminum alloy (A5052) and plain woven CFRTP. The lay-up of the CFRTP was [(0,90)]9 and the used matrix was PA6. Fatigue loading was applied in displacement control mode. The ratio between the minimum and maximum displacement was 0.1, and the test frequency was 5 Hz. The crack length during the fatigue tests was obtained by compliance calibration. Fatigue was characterized by constructing a Paris diagram for each specimen type. The fracture surface distinctively changed from smooth brittle-like fracture to hair-like ductile fracture post fabricating a nanostructure and chemical bonding. As a result, the fatigue crack growth resistance of the specimen with the nanostructure significantly improved due to the hair-like ductile fracture. [ABSTRACT FROM AUTHOR]

A cohesive zone model for delamination propagation in laminated composites under static and fatigue loading has been derived and validated with experimental data under different mode conditions. This study presents a new approach to quantify fatigue delamination degradation based on damage mechanics to evaluate the rate of fatigue damage ( ∂ D / ∂ N ). The static damage evaluation and fatigue damage degradation are derived from damage surface concept. Both static and fatigue damage linked each other to establish fatigue crack growth formula in the laminated composites. A user-defined subroutine, UMAT, has been employed to develop and implement a damage model in ABAQUS. Two different specimens; a double cantilever beam and a single lap joint were used to investigate the effectiveness of the new method. The simulation results revealed that the developed model had good agreement with experimental data available in literature. [ABSTRACT FROM AUTHOR]

Fatigue delamination growth (FDG) is an important failure in composite structures during their long-term operations. Hygrothermal aging can have significant effects on interlaminar resistance. It is therefore really necessary to explore FDG behavior in composite laminates with hygrothermal aging. Dynamic mechanical thermal analysis (DMTA), mode I FDG experiments and fractographic examinations were conducted to fully investigate hygrothermal aging effects and the corresponding mechanisms on FDG behavior. The DMTA results indicated that environmental aging can induce obvious T g decrease. Mode I experimental fatigue data interpreted via different Paris-type correlations demonstrated that: Bridging has obvious retardation effects on FDG behavior via the Paris interpretations; The modified Paris relation can well characterize the intrinsic FDG behavior around the crack front; The use of the two-parameter Paris-type relation can appropriately account for R -ratio effects, contributing to a master resistance curve in determining mode I FDG behavior. According to these interpretations, it can be concluded that hygrothermal aging can have adverse effects on mode I FDG behavior. SEM examinations demonstrated that moisture absorption can cause fibre/matrix debonding and resin matrix pores/voids in the composite. However, no obvious difference in damage mechanisms was identified in mode I fatigue delamination for composite with/without environmental conditioning. Both fibre/matrix debonding and matrix brittle fracture were identified on fatigue fracture surfaces. Accordingly, it was concluded that fibre/matrix interface and matrix degradation induced by water absorption were the main reasons for a faster mode I fatigue crack growth in environmental aged composite. [ABSTRACT FROM AUTHOR]

• Effect of hybrid laminate configuration on fatigue crack growth has been investigated. • Mode partition by Valvo (MPV) and modified beam theory (MBT) are used in evaluating crack growth. • MBT falls short of mode-mixity with higher exponent of Paris law as compared to MPV method. • G ^ Imax and Δ G ^ Ieff as crack driving parameters are used to quantify fatigue crack growth. • MPV method is found to be not sensitive to G ^ Imax and Δ G ^ Ieff for displacement ratio of 0.1. Effect of similar and dissimilar crack plane interface configuration on fatigue delamination growth in plain woven hybrid composite laminates under Mode-I has been investigated. Constant displacement amplitude fatigue testing with displacement ratio of 0.1 was carried out on 3 configurations of plain woven glass/carbon epoxy composite laminates. A power law like fit between recorded delamination length and corresponding cycle was used to predict crack length for each of the cycle. Delamination growth rate, da / d N is computed by differentiating the expression of power-law like fit. The obtained crack growth rate for each of the specimens were plotted with respect to two normalised functions, G ^ Imax = G Imax (a) / G IR (a) where G Imax is maximum mode-I energy release rate and G IR (a) is the interlaminar fracture toughness resistance and Δ G ^ Ieff = G ^ Imax - G ^ Imin 2 as crack driving parameters computed on the basis of Modified Beam Theory (MBT) and Valvo's mode partition method (MPV) are used in Paris relation to quantify delamination propagation. It is observed that the exponent values predicted by MBT method for G ^ Imax is lower as compared to Δ G ^ Ieff . Whereas, exponent values predicted for G ^ Imax is higher as compared to Δ G ^ Ieff predicted by MPV method. The higher the exponent value, the higher is the sensitivity of the model leading to uncertainties in the crack growth prediction. Also, it is to be noted that cyclic loading effect is when both G Imax and G Imin is considered, the use of Δ G ^ Ieff as crack driving parameter to quantify delamination propagation is justified. Secondly, MBT method does not account for the mode-mixity arising due to hybrid material configuration as in the case of Local Symmetry Fatigue (LSF) and Asymmetry Fatigue (ASF) specimens. Hence, results in higher exponent as compared to MPV method. On the other side, the G ^ Imax and Δ G ^ Ieff computed on the basis of MPV method is the pure Mode-I component deduced from the total energy release rate of mode-mixity. The equations of curve fitting is very much the same for Simple Symmetry Fatigue (SSF) specimens indicating that MBT and MPV methods predict pure Mode-I behaviour for symmetric configuration for delamination growth under fatigue Mode-I loading. From the composite laminate configuration point of view, LSF specimens have higher exponents as compared to ASF and SSF specimens indicating, local symmetry configuration laminates are highly sensitive to the small uncertainties and results in unstable crack growth. Comparison of results of all hybrid composite laminates shows that the normalised functions of G ^ Imax and Δ G ^ Ieff as crack driving parameters computed on the basis of MPV method is able to capture the effect of interlayers and stacking effect on the delamination growth in hybrid plain woven composites in fatigue loading and MPV method is found to be not sensitive to G ^ Imax and Δ G ^ Ieff for displacement ratio of 0.1. [ABSTRACT FROM AUTHOR]

• Temperature has significant but different effects on the mode I intrinsic fatigue delamination resistance at the crack front and fibre bridging development in the wake of the crack front. • Physical reasons for the difference in temperature dependence of the intrinsic fatigue delamination resistance and fibre bridging development have been explored and discussed. • A semi-empirical fatigue model accounting for data scatter has been successfully proposed to represent the intrinsic FDG behavior at different temperatures. • This study provides solid evidence on the validity of using the modified Paris relation in fibre-bridged fatigue delamination characterization, which is useful for developing mode I fatigue delamination test standard of composites. Temperature can significantly affect fatigue delamination growth (FDG) behavior in composites, while fiber bridging has been frequently reported during FDG. The focus of this study was therefore on investigating temperature effects on FDG behavior with fiber bridging. Mode I fatigue delamination experiments were conducted on a thermoset composite laminates M30SC/DT120 at different temperatures. The Paris relation and fatigue resistance curve (i.e. fatigue R -curve) were used to interpret bridging effects on FDG behavior and to explore temperature effects on fiber bridging development. A modified Paris relation was employed to determine the effects of temperature on the intrinsic FDG behavior at the crack front excluding fiber bridging. The Paris interpretations clearly demonstrate that fiber bridging can significantly retard FDG behavior at different temperatures. Temperature can have different effects on fiber bridging development and the intrinsic FDG behavior. Particularly, elevated temperature can promote more bridging fibers, whereas decreased temperature has negligible influence on fiber bridging. When looking at the intrinsic delamination resistance, mode I FDG can accelerate at elevated temperature but decrease at freezing temperature. Fractographic examinations indicate that fiber/matrix interface debonding is the dominant damage mechanism in mode I FDG at different temperatures. Elevated temperature can lead to the weakening of interface adhesion, contributing to faster intrinsic mode I FDG behavior and more fiber bridging development. And a semi-empirical fatigue model based on normalization was finally proposed to determine mode I intrinsic FDG behavior at different temperatures for engineering applications. [ABSTRACT FROM AUTHOR]

An experimental investigation of mode‐I translaminar fracture toughness and fatigue crack growth behavior of a carbon fiber‐epoxy plain weave laminate manufactured by resin infusion under flexible tooling (RIFT) is presented in this article. Pre‐cracked compact tension (CT) specimens were used to perform both quasi‐static and fatigue tests. Different data reduction techniques for fracture toughness calculation were used and compared with each other. The ASTM E399 test method was modified to account for the material orthotropy and specimen geometry effects using a correction function based on a numerical evaluation of the strain energy release rate. The proposed modification shows good agreement against other experimental methods found in the literature and its application was validated for fatigue tests. Fatigue testing shows that failure in undesired modes is likely to occur prior to translaminar fracture, which was attributed to a higher tensile fatigue threshold than compression or shear fatigue threshold presented by the composite in analysis. Increasing the specimens' initial notch length was a solution for avoiding these types of failure. The experimental results were compiled in the form of a Paris curve, and their particularities were discussed. A fractographic analysis was carried out to define damage patterns and its evolution process in both types of tests. POLYM. COMPOS., 40:3791–3804, 2019. © 2019 Society of Plastics Engineers [ABSTRACT FROM AUTHOR]

Double cantilever beam (DCB) specimens composed of carbon fiber reinforced polymer laminate composites were tested. Two material systems were investigated. One consisted of plies from a woven prepreg alternating with tows in the 0 ∘ / 90 ∘ -directions and the + 45 ∘ / - 45 ∘ -directions. The second was fabricated by means of a wet-layup process with the same multi-directions as the prepreg. In addition, for the second material system, a unidirectional (UD) fabric ply was added. The delamination for this laminate was between the UD fabric and the woven ply with tows in the + 45 ∘ / - 45 ∘ -directions. Both fracture resistance R-curve and fatigue delamination propagation tests were carried out. It is found that the initiation value of the interface energy release rate is substantially lower for the wet-layup; whereas, their steady state values are quite similar. The fatigue delamination propagation tests were performed at various cyclic R-ratios. The delamination propagation rate da/dN was calculated from the experimental data and plotted using a modified Paris equation with different functions of the mode I energy release rate. As expected, the da/dN curves depend upon the R-ratio. By using another parameter based on the Hartman–Schijve equation for metals, it is possible to obtain a master-curve for all R-ratios. It is seen that the propagation rate for the prepreg is faster than that of the wet-layup. [ABSTRACT FROM AUTHOR]

• A neural network is utilized to enable simulation of fatigue damage propagation using cohesive elements (NFCOH) with improved degradation formulation. • Physics-informed regulation terms deduced from Paris-law is applied to help the neural network learn from small data. • The NFCOH model is insensitive to the interfacial strength parameters due to the use of a compensation scheme. • The NFCOH model is applied to predict the fatigue life of open-holed composite laminates with good accuracy. Recent developments in machine learning technologies offer new insights for solving traditional engineering problems as well as a new data-driven framework for novel in-situ material characterization scheme. However, the need for large training samples severely limits the applicability of models of this nature. In this work, a novel training strategy utilizing Paris law is proposed for a neural fatigue cohesive (NFCOH) model. By adding regulation terms deduced from Paris law to the loss function of the neural network, the number of training samples required for NFCOH is significantly reduced. In addition, compensation methods for interfacial strength parameters are also proposed and investigated to further increase the flexibility of NFCOH. Finally, the NFCOH model is utilized to predict the fatigue life of complex open-holed composite laminates to demonstrate the effectiveness of the model where good correlations between the numerical predictions and experimental measurements are achieved. [ABSTRACT FROM AUTHOR]

Efficient yet reliable predictive modelling tools for damage tolerance analysis became an aerospace industry requirement as composite materials provided the potential for design performance. As damage can be separated into interlaminar and intralaminar, different approaches were developed over the years. For fracture analysis of intralaminar damage, a physical link to the Linear Elastic Fracture Mechanics (LEFM) provides a reliable framework for Continuum Damage Mechanics (CDM) models. These models, however, may exhibit pathological problems related to mesh dependence, objectivity and convergence issues. Differently from Cohesive Zone Modelling (CZM) for interlaminar damage, most intralaminar models are based on phenomenological approaches for fatigue analysis and life prediction. This work provides a description of some of the current intralaminar CDM models shortcomings, related to large strain analysis and finite element topology. A novel progressive damage model is proposed where damage variables are linked to the deformation gradient. Additionally, a fatigue damage behaviour under the assumption of a Paris law for crack evolution is implemented in the proposed methodology. Both static and fatigue analysis were performed on a Compact Tension (CT) specimen geometry and compared to experimental data available on the scientific literature. Model predictions and experimental data were confronted allowing for conclusions to be drawn. • Discussion on shortcomings of strain-based damage variables at finite displacements. • Novel damage variable expression based on the integration point deformation gradient. • Novel characteristic length for reduced integration rectangular shell elements. • Novel progressive damage model for fatigue assuming a Paris law for crack evolution. [ABSTRACT FROM AUTHOR]

[Display omitted] • A neural cohesive element model is proposed for simulating delamination under cyclic loadings. • A single-hidden-layer neural network functions as the constitutive law for updating fatigue damage to enforce delamination propagation. • Benchmark models under both pure-mode and mixed-mode loadings are given with good correlations between theory and FE simulations. • The model shows high computational efficiency and insensitivity to mesh size, both beneficial for complex structural analysis. This work proposes a novel fatigue cohesive model that utilizes a single-hidden-layer neural network as its fatigue constitutive law for simulation of fatigue delamination under mixed-mode loadings. The neural network takes variables of the cohesive zone as inputs and outputs the accumulation rates for a fatigue damage variable to enforce fatigue delamination propagation, which is then embedded in Abaqus to verify the model under mode-I, mode-II and mixed-mode loadings with Paris law and Hartman-Schijve equation as references. On top of the good correlations, it is found that the proposed model is also insensitive to mesh sizes and very computationally efficient. [ABSTRACT FROM AUTHOR]

A cohesive zone model (CZM) for fatigue crack propagation was integrated within the Regularized eXtended Finite Element Method (Rx-FEM) discrete damage modeling framework. This CZM constitutive model, which is formulated in terms of S-N stress-life curves rather than the more usual rates of crack propagation described with a Paris law, can predict both crack initiation and propagation by relying on the intrinsic relationships between S-N and the Paris law. This feature of the model is of significant practical interest since S-N curves can be synthesized with few parameters and simple engineering assumptions, while the experimental characterization of the Paris law parameters for all required stress ratios, mode mixities, and material interfaces in a composite structure is very difficult and often impractical. Used in combination with the Rx-FEM method, this CZM can predict mesh-independent crack networks in composite structures subjected to cyclic or quasi-static loads. The Rx-FEM methodology for fatigue damage was implemented in Abaqus using two superimposed sets of standard Abaqus elements to represent the enriched displacement field. The capabilities of the proposed methodology are demonstrated by comparing the experimental and predicted response of a mixed-mode bending (MMB) test, as well as a Clamped Tapered Beam (CTB) sub-element designed to study matrix crack initiation, delamination propagation, and subsequent delamination migration from one ply interface to another. [ABSTRACT FROM AUTHOR]

The objective of this work is to perform fatigue/fracture characterization of carbon-epoxy laminates under pure mode II loading. The End-Notched flexure (ENF) test was employed to execute quasi-static and fatigue/fracture tests aiming to determine the mode II fracture energy, the fatigue lives and the modified Paris law parameters representative of this material. These Paris law coefficients were used as input in a high-cycle fatigue cohesive zone model that was validated against experimental fatigue lives. Afterwards, the numerical cohesive zone model was employed to assess the influence of several geometrical and material parameters on the mode II interlaminar fatigue/fracture behaviour of Carbon-Fibre Reinforced Plastic (CFRP) laminates. Important conclusions were drawn concerning the fatigue performance of these materials under pure mode II loading. [Display omitted] [ABSTRACT FROM AUTHOR]

We propose to treat propagation of a fatigue-driven delamination in composite laminates as a sequence of incremental delamination onsets and develop a cohesive zone model (CZM) to simulate it. The model employs a fatigue damage evolution law that is based on the reduction of critical strain energy release rate. Unlike existing fatigue CZMs, which assume and use Paris' law derived from propagation tests as input, the proposed model relies solely on the experimental data from fatigue onset tests (namely the G-N curve, where G is the supplied strain energy release rate and N is the number of cycles to onset). The model is implemented within an implicit finite element code using three-dimensional cohesive elements and is demonstrated to predict fatigue delamination propagation in unidirectional carbon fibre/epoxy composites under Mode I loading. This incremental onset model predicts the Paris' law, which compares well with experimental data for this case. Composites with toughened inter-laminar interface and under other modes of deformation and their combinations may exhibit a different fatigue behaviour. Image 1 [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on the energy release rate (ERR) extractions and mixed mode behavior of fatigue cohesive model. The development of the non-linear cohesive zone ahead of a crack tip is influenced by multiple factors, where the extractions of ERRs and mode ratios are crucial for accurate fatigue analysis in Paris law-based models. Investigations into the effects of different parameters e.g. interfacial strengths, shapes of the cohesive laws and element sizes on the extracted ERRs are conducted. In addition, two novel mixed mode bending models i.e. multi-stage mode ratio (MSMR) and continuously various mode ratio (CVMR) models are proposed for mixed-mode behavior study. All results are compared to the theoretical fracture mechanics analysis and to each other. It is found that if the interfacial strength becomes too low, an excessively long cohesive zone can form, where the mode ratio could significantly deviate from the true value and negatively impact the accuracy. The shape of cohesive laws is also found to influence the ERRs and mode ratios to some extent but are not the dominating factor. [ABSTRACT FROM AUTHOR]

Cohesive zone modelling (CZM) has been extensively considered as a powerful method for analysis of initiation and propagation of delamination in composite laminates subjected to cyclic loading. By making a relation between the damage parameter and the loading cycles, damage accumulation can be calculated, and the fatigue life of a component can be estimated. The aim of the current research is to present a new fatigue damage accumulation (FDA) model. The proposed model is developed based on the concepts of CZM and by linking the fracture mechanics to damage mechanics approaches. For this purpose, a developed user material subroutine (USDFLD) is implemented in a finite element software to simulate the initiation and propagation of damage in an interface layer of a composite material subjected to cyclic loading. The method is validated for different loading conditions using Paris law results. Good agreement between the proposed method and the Paris law results is observed. [ABSTRACT FROM AUTHOR]

• Fatigue delamination growth by End Notch Flexure tests in mode II. • Delamination growth in glass and carbon reinforced fiber metal laminates. • Presence of compressive stresses in the region of force application. • Retardation of fatigue delamination growth caused by compressive stresses. • Modified Paris curves db/dN vs. G II(max) for Al/CFRP and Al/GFRP interfaces. Fatigue delamination growth (FDG) rate was investigated in composite laminates with aluminium and carbon/glass fibers. An End Notch Flexure test was used to determine compliance-calibration as well as fatigue and quasi-static interlaminar fracture. Experimental tests results suggest, that fatigue delamination threshold in a metal-composite interface is governed by the epoxy matrix, while the FDG rate is governed by the fibers/matrix cohesion. Deceleration of delamination growth was observed when delamination reached a central point of the specimen. Generally, laminates reinforced by glass fibers are more resistant for delamination growth than reinforced by carbon fibers. [ABSTRACT FROM AUTHOR]