Fatigue Life Of Composite Laminates Research Articles

Modelling the residual strength degradation in composite materials without using residual strength tests

Residual strength models are widely used to predict the fatigue life of composite laminates under highly variable loads. However, they often require considerable experimental effort to accurately determine model parameters. This paper introduces a new approach for predicting the residual strength of composite materials with less experimental data. The method is based on two common strength-based wearout models, the Sendeckyj model and Schaff and Davidson model. The Sendeckyj model consists of an equation with two model parameters, which describes the shape of the S-N curve by fitting fatigue test data. The Schaff and Davidson model is a single-parameter function which calculates the residual strength based on the number of fatigue cycles. Using a novel mathematical algorithm, the residual strength model parameter in the Schaff and Davidson model is estimated directly from the S–N curve without running any residual strength tests. Five data sets from the literature are used to validate the new methodology. The results show that the residual strength model parameter is dependent on both the stress level and the number of loading cycles experienced at this stress level, both of which are considered in the new strategy. In addition, if the fatigue data are well distributed, the residual strength model parameter estimated by the new strategy is close to the experimental data.

Cumulative Fatigue Damage of Composite Laminates: Engineering Rule and Life Prediction Aspect.

The analysis of cumulative fatigue damage is an important factor in predicting the life of composite elements and structures that are exposed to field load histories. A method for predicting the fatigue life of composite laminates under varying loads is suggested in this paper. A new theory of cumulative fatigue damage is introduced grounded on the Continuum Damage Mechanics approach that links the damage rate to cyclic loading through the damage function. A new damage function is examined with respect to hyperbolic isodamage curves and remaining life characteristics. The nonlinear damage accumulation rule that is presented in this study utilizes only one material property and overcomes the limitations of other rules while maintaining implementation simplicity. The benefits of the proposed model and its correlation with other relevant techniques are demonstrated, and a broad range of independent fatigue data from the literature is used for comparison to investigate its performance and validate its reliability.

Multiscale fatigue damage model for CFRP laminates considering the effect of progressive interface debonding

This paper presents a multiscale progressive fatigue damage model to predict the fatigue life of composite laminates. The multi-level damage model was employed considering the interfacial debonding effect, and effective material properties were calculated through homogenization. Damage variables and damage slopes were defined at the constituent level, and fatigue damage parameters were obtained using the residual stiffness data with the chaotic firefly algorithm. The model was implemented into ABAQUS, then validated with flat-bar and pin-loaded specimens of AS4/3501-6 composite. The numerical results corresponded well with the experimental data and showed the ability to capture the failure propagation of composite laminates.

Fatigue life prediction of CFRP laminates with stress concentration lamina level failure criteria

This paper presents a progressive fatigue damage model to predict the damage progress and the fatigue life of composite laminates under cyclic loading. First, the maximum stress criterion was applied in the fiber direction for fiber failure (FF), and Puck’s failure criteria were employed in the matrix direction in which the fracture plane is defined to determine the inter-fiber fracture (IFF). Next, material degradation rules consisting of strength and stiffness degradation were derived, and different degradation rules according to the presence of failure and failure mode were utilized for each material. The proposed model was implemented into the UMAT subroutine of ABAQUS for the finite element (FE) analysis with tension–tension cyclic loading. Finally, the progressive fatigue damage model was validated with flat-bar specimens with various lay-ups ([0]8, [90]8, [30]16, [02/902]s, [0/902]s, [0/904]s) and compared with the experimental data of static and fatigue tests. The fatigue life prediction was also conducted on the pin-loaded quasi-isotropic (QI) laminates. The simulation results showed a good agreement with the experimental data and the ability to capture the damage progress of composite laminates during their lifetime.

A Multiaxial Fatigue Damage Model Based on Constant Life Diagrams for Polymer Fiber-Reinforced Laminates.

In the last decade, fatigue damage models for fiber-reinforced polymer composites have been developed assuming the fracture energy equivalence hypothesis. These models are able to predict a fatigue life of composite laminates, but their identification requires a significant number of off-axial tests for various stress ratios. The present study proposes the stress ratio dependent model, which phenomenologically adopts a decrease in stiffness and residual strength of a unique ply according to experimental constant life diagrams. Hashin, Tsai-Hill, and the maximum stress failure criteria are utilized for damage initiation considering the residual strength of the ply. The obtained results indicate a sufficiency of using S-N curves for UD 0°, UD 45°, and UD 90° for identification of the model. The model was verified by S-N curves for UD 10°, UD 15°, and UD 30° and its applicability was demonstrated for prediction of a fatigue life of composite laminates with an arbitrary lay-up. The model is implemented into ABAQUS finite element software as a user subroutine.

Probabilistic fatigue model for composites based on the statistical characteristics of the cycles to failure

A probabilistic model for estimating the fatigue life of composite laminates based on the mean value and standard deviation of the fatigue life is introduced here for predicting the distribution of fatigue life at any stress level for a constant stress ratio. The proposed model is validated with experimental data for several composite materials, and its accuracy is evaluated by goodness-of-fit-statistical tests. The proposed second-order polynomial model can be used to develop probabilistic constant life diagrams and probabilistic S-N curves for any stress ratio which are corroborated well by available experimental data.

A reliable progressive fatigue damage model for life prediction of composite laminates incorporating an adaptive cyclic jump algorithm

In this paper, a reliable progressive fatigue damage model (PFDM) for predicting the fatigue life of composite laminates is proposed by combining the normalized fatigue life model, nonlinear residual degradation models and fatigue-improved Puck criterion. To balance the accuracy of life predictions and computational efficiency, an adaptive cyclic jump algorithm is developed and implemented within the PFDM. The sensitivity of life prediction to cyclic jump parameter has been greatly reduced by correlating the cyclic jump with the increment time and viscous coefficient. Therefore, the cyclic jump parameter can be arbitrarily selected within a relatively large range to obtain convergent results. When incorporating the adaptive cyclic jump algorithm, there is no need to define a standard for determining the material failure in numerical calculations, which effectively eliminates an artificially induced uncertainty in life predictions. Two sets of experiments are conducted to validate the proposed PFDM. The numerical predictions including static failure strength and fatigue life correlate reasonably well with the available experimental data.

Strength and stiffness degradation modeling and fatigue life prediction of composite materials based on a unified fatigue damage model

The performance degradation of composite materials under fatigue loading is so complex that the present knowledge is far from complete. This study aims to present a pair of residual strength and residual stiffness models based on a unified fatigue damage formula, and predict fatigue life under variable amplitude cyclic loading. Firstly, a unified fatigue damage model for composite materials is proposed, which is capable of characterizing fatigue damage development caused by strength degradation and stiffness degradation, respectively. Subsequently, a pair of residual strength and residual stiffness models is presented to estimate the performance degradation of composite materials. Finally, the corresponding life prediction methods are developed from the viewpoints of strength degradation and stiffness degradation, respectively. A set of experimental data for composite laminates are utilized to validate the proposed models and methods. The results show that the proposed residual strength and stiffness models are flexible enough to fit strength and stiffness degradation data with good agreement. Moreover, the developed life prediction methods are capable of calculating fatigue life of composite laminates with high accuracy.

Stochastic fatigue life prediction of Fiber-Reinforced laminated composites by continuum damage Mechanics-based damage plastic model

In this paper, the evolution of elastic–plastic damage in the composite laminates under fatigue conditions is modeled. Continuum damage mechanics (CDM) has been coupled with the bridge micromechanics model to estimate the fatigue damage and life for laminated composite structures. Based on the elastic–plastic bridging model, three damage variables are defined. These variables estimate the fiber, matrix, and fiber/matrix damage response at the ply scale. To model the beginning of plastic deformation, a yield function is utilized, and evolution equations of the damage variables are obtained. Then the developed deformation plastic model is calculated. The model parameters are calibrated by experimental data. The proposed model is implemented in Abaqus by a subroutine. The capability of the developed model under multiaxial loading is investigated. The constitutive behavior of composite laminates in different conditions is compared with experimental data. The estimated fatigue life of the CDM-plastic damage approach for different layups is in accordance with the experimental data. Numerical results confirm the plastic deformation model leads to more accurate fatigue life prediction, especially in low‐cycle fatigue. Finally, a stochastic model is applied to predict the fatigue life of composite laminates. In the stochastic approach, fiber volume fraction, critical damage parameters, and mechanical properties are modeled as random variables with normal distribution. The stochastic model emphasizes the importance of variations of mechanical properties.

A Continuum Damage Mechanics-based Piecewise Fatigue Damage Model for Fatigue Life Prediction of Fiber-Reinforced Laminated Composites

The purpose of this study is to define a piecewise fatigue damage model (PFDM) for the prediction of damage in composite laminates under cyclic loading based on the continuum damage mechanics (CDM) model. Assuming that damage in fiber-reinforced plastic structures accumulates nonlinearly, a piecewise degradation growth function is defined and coupled with CDM and micromechanics approaches. The model divides the damage behavior of fiber, matrix, and fiber/matrix debonding at the ply scale, into three different stages. For generality, a fully multi-stage damage formulation on a single-ply level is employed. The unknown parameters of the PFDM are estimated according to obtained experimental data of damage mechanisms associated with the composites laminate under cyclic loading. To predict multidirectional composite laminates' fatigue life, the proposed model was implemented in Abaqus software by the subroutine. In a validation against experimental data on carbon fiber reinforced material, the model proves to provide a good numerical approximation of the damage during the fatigue loading. The results reveal that by considering the multi-stage process in stiffness reduction, the proposed model can estimate the fatigue life of composite laminate under multiaxial cyclic loading conditions more accurately than the similar model in the literature.

Equivalent Spectral Method to Estimate the Fatigue Life of Composite Laminates Under Random Vibration Loadings

The power spectral density (PSD) of an equivalent stress is proposed to analyze the fatigue life of composite laminates under random vibration loadings using the Tsai–Hill criterion. The vibration fatigue life can be estimated based on the rainflow amplitude probability density function p(S) of the equivalent stress, which is obtained from this PSD, combined with the S-N curve of the materials. The fatigue life analysis of a random vibration fatigue experiment of composite laminates was carried out, and the calculation results were in accordance with experimental data, which indicates that the fatigue life analysis model proposed gives a satisfactory prediction accuracy.

Multiaxial fatigue life prediction of composite laminates

A study of composite laminates under tension–torsion biaxial loading is presented. The focus is placed on fatigue lives of composite laminates under different tension–torsion biaxial fatigue loading paths. A macro-meso model used to predict multiaxial fatigue life of composite laminates is also presented in this paper. Firstly, a macro-scale 3D RVE corresponding to composite laminates is established to determine strain components in the material principal direction of each layer for each biaxial stress ratio. Secondly, a meso-scale 3D RVE corresponding to each layer with fibers distributed randomly is established, with progressive damage prediction method, biaxial strength of composite laminates can be predicted, and the final failure layer can be confirmed. Thirdly, select any one of fatigue loading path at which the final failure of composite laminates is fiber failure (matrix failure) to establish the reference curve for fiber (matrix). Finally, with reference curve, fatigue life of composite laminates under any biaxial loading path can be predicted. And numerical results show good agreements with experimental data.

Fatigue life prediction of composite laminates by fatigue master curves

In this paper, fatigue master curves are adopted to predict fatigue life of composite laminates made by unidirectional and braided fiber reinforced composite. Fatigue failure is then determined by Puck’s criterion. Uniaxial and multiaxial S-N curve could be obtained from the fatigue master curves. Fatigue lives of composite laminates made by unidirectional carbon and glass fiber reinforced composite are predicted by the proposed method. To extend the fatigue master curve to predict the braided composite laminate, tensile-tensile, compressive-compressive and tensile-compressive fatigue experiments are carried out in this paper. The predictions from the proposed fatigue model are compared with various experimental results and reasonably good agreement is observed.

On the evaluation of damage-entropy model in cross-ply laminated composites

Entropy production during cyclic loading can serve as a measurement of degradation for composite materials. The results of a series of experiments on 0° plies, 90° plies and cross-ply laminates of carbon/epoxy are presented to characterize the fatigue behavior in terms of temperature evolution, hysteresis energy and the entropy associated with the damage and irreversible deformations. A theoretical approach based on the first and second laws of thermodynamics is presented which takes into account the damage energy, the work of irreversible deformations and the dissipated heat due to the viscoelastic nature of the polymeric matrix. The experimental and analytical results show that the concept of tallying up entropy owing to damage and irreversible deformations until final failure is useful to predict the fatigue life of composite laminates. The fatigue fracture entropy values of fiber and matrix, so-called FFE-F and FFE-M in this study, are considered as final failure criteria for 0° and 90° plies, respectively. The results of entropy accumulation indicate that interpretation of fatigue behavior of laminated composites requires to consider both the entropy associated with damage and irreversible deformations.

Fatigue life prediction and modal analysis of carbon fiber reinforced composites

Fiber reinforced composite materials are finding increasing applications in aerospace structures, naval industry, military and automotive industry, because of their high specific stiffness and strength. The fatigue of composite materials is not completely understood which is quite different from metal fatigue. The objective of research is to apply modal testing for the fatigue life prediction of Carbon Fiber Reinforced Plastic laminate in plane bending with different fiber orientations. CFRP laminates with three fiber orientations as 0°, 45° and 90° are applied to fatigue loading in plane bending with R = -1 and S-Nf. curves are plotted and power equations are determined. For modal testing of the laminates the specimens previously undergone fatigue loading are tested at specific intervals to determine the effect of modal characteristics on fatigue life of these laminates. The modal characteristics are determined by using FFT analyzer and the frequency effect on fatigue life is determined. Results are plotted between the fatigue life ratio and the natural frequency and empirical equations are generated for predication of fatigue life prediction. From the results it is concluded that the modal testing is an effective nondestructive testing method that can be applied for estimating the fatigue life of composite laminates

The Effect of Metal on Composites Fatigue Damage in Mixed Structure

This paper investigated the fatigue damage coupling of composite laminate and metallic plate in multi-bolt joint. A progressive fatigue damage model for composite laminates and a modified Lemaitre damage model for metal material were developed. A phenomenological elastoplastic constitutive model was used to describe the in-plane shear nonlinearity of composite lamina. A formula for calculating the energy release rate of the low cycle fatigue was derived based on spherical tensor and shear tensor decomposition of the stress. The developed models were validated by the experimental results of a double-lap single-bolt metal-composite joint and were employed to simulate the fatigue damage of a double-lap, multi-bolt metal-composite joint. The result indicates that fatigue damage will harden the materials nearby the bolt region of the metallic plate for a multi-bolt joint structure when suffering to cyclic loads. This hardening behavior results to a transfer of bolt loads towards the harden region, which intensifies bearing damage and reduces tensile stress in the composite laminate, and improves the fatigue life of composite laminates fail in tensile mode.

Random fatigue life prediction of carbon fibre-reinforced composite laminate based on hybrid time-frequency domain method

To evaluate fatigue life of composite laminate with hole under random loading, a random fatigue life prediction model is established by hybrid time-frequency domain method in this paper. Firstly, dynamic response of composite laminate is obtained from FE model in frequency domain. Secondly, root mean square of stress of six stress components of critical damage point in frequency domain are transferred to stresses in time domain. At last, 3D Tsai–Hill static failure criterion is adopted to convert the multiaxial stress into the uniaxial equivalent stress. Fatigue life is predicted by equivalent stress fatigue life code. The method is validated with the random vibration fatigue test of carbon fibre-reinforced composite laminate. Numerical results are compared with random fatigue experiments which show good agreement with numerical results.

Fatigue life prediction of laminated composites using a multi-scale M-LaF and Bayesian inference

This paper presents a probabilistic model for fatigue life estimation of composite laminates using a high fidelity multi-scale approach called M-LaF (Micromechanics based approach for Fatigue Life Failure). To this end, square and hexagonal representative unit cells are introduced to calculate constituent stresses using a bridging matrix between macro and micro stresses referred to as the stress amplification factor matrix. The M-LaF is based on the constituent level input data that makes it possible to predict fatigue life of a variety of laminates with any possible fiber volume fraction. The M-LaF model parameters are calibrated as posterior distribution using the Bayesian inference methodology. A reference test data from literature was used for parameter calibration. The calculated posterior statistics were then used to calculate probabilistic fatigue life estimates of sample laminates. The predicted S–N curves are in good agreement with the test data for a range of composite laminas as well as laminates with different fiber volume fractions and under diverse stress ratios. As an illustration, the above approach was applied to a wind turbine blade to show the effect of multi-axial loading on the fatigue life of composite laminates.

A multiscale approach for fatigue life prediction of polymer matrix composite laminates

The present study introduces a progressive fatigue damage model within a multiscale framework by incorporating a Simplified Unit Cell Micromechanical model into a Finite Element program. The use of micromechanics will allow the study of damage at the micro-scale which can therefore identify modes of failure in each of the composite’s constituents, separately. The use of finite element method at the macro-scale enables the model to capture the geometric complexities including regions of stress concentration, which expedites the failure of the material. Damage progression is modeled through the degradation of the material property corresponding to the failure mode detected by the micromechanical model. The results of the model are in good agreement with the experimental data for both unidirectional and multidirectional laminates. The present approach is capable of predicting the fatigue life of composite laminates of any arbitrary geometry and lay-up configuration with minimum dependence on empirical parameters.

Experimental Investigation on the Tensile Strength of Composite Laminates Containing Open and Filled Holes

An experimental study is performed to evaluate the effects of clamping pressure, friction, and washer size on the static performance of composite laminates with open and bolt-filled holes. The static tensile strength and failure behavior of composite laminates with an open hole and a bolt-filled hole are analyzed and compared. Experimental results show that the static tensile strength of composite laminates is sensitive to pre-existing damage of both open- or filled-hole laminates. In contrast, a comparison between the experimental results of open- and filled-hole specimens proved that whether the hole is open or filled has a feeble influence on the tensile-tensile fatigue strength of studied composite laminates. In comparison, however, it is found that the inserted washer size, bolt clamping force, and friction force strongly affect the tensile strength of open- and filled-hole composite laminates. Moreover, application of thicker washers and hi-lock bolt will significantly increase the static strength and fatigue life of composite laminates with a bolt-filled hole.