A micro-mechanics damage approach for fatigue of composite materials

A new model for fatigue damage evolution of polymer matrix composites (PMC) is presented. The model is based on a combination of an orthotropic damage model and an isotropic fatigue evolution model. The orthotropic damage model is used to predict the orthotropic damage evolution within a single cycle. The isotropic fatigue model is used to predict the magnitude of fatigue damage accumulated as a function of the number of cycles. This approach facilitates the determination of model parameters since the orthotropic damage model parameters can be determined from available data from quasi-static-loading tests. Then, limited amount of fatigue data is needed to adjust the fatigue evolution model. The combination of these two models provides a compromise between efficiency and accuracy. Decomposition of the state variables down to the constituent scale is accomplished by micro-mechanics. Phenomenological damage evolution models are then postulated for each constituent and for the micro-structural interaction among them. Model parameters are determined from available experimental data. Comparison between model predictions and additional experimental data is presented.     

The effect of composite damage on fatigue life of the high pressure vessel for natural gas vehicles

In order to examine how the damages such as scratches, cuts and gouges on the composite materials have effects on the fatigue life of NGV vessels, several experiments on real vessels were conducted and finite element analyses were applied. The flaw depths of COPV used in the experiments were 1.5 mm, 2.0 mm, 3.0 mm, and 4.0 mm, while the flaw lengths were 50 mm, 100 mm, and 200 mm. A flaw tolerance test defined by ANSI/IAS NGV2-2000 was performed on 12 vessels using a combination of these flaw depths and lengths. In the finite element analyses, stress analyses were performed using a commercial FEM program after the 3-D modelling of liner, hoop and helical layers by using MSC.PATRAN™. The result of the tests and analyses demonstrated that the effect of the flaw damages on the fatigue life of high pressure vessel for natural gas vehicles increases when the flaw depth is more than 3.0 mm and the flaw length is more than 100 mm.     

A statistically consistent fatigue damage model based on Miner’s rule

With Monte Carlo sampling method, a statistically consistent fatigue damage model under constant and variable amplitude loadings based on linear Miner’s rule is proposed, which can quantitatively depict the probabilistic properties of fatigue damage and life. Numerical simulation shows that linear Miner’s damage criterion is statistically inconsistent; through some modification from a probabilistic point of view, a statistically consistent damage criterion is first established. To validate the statistical model, numerical verification of a supposed two-level cyclic loading and experimental verification of fatigue tests for Al-alloy straight lugs available in the literature are successfully conducted. The model predictions coincide quite well with both engineering hypotheses and experimental observations, compared with Miner’s model, indicating that the model can be regarded quantitatively accurate for engineering application.     

Characterization of fatigue damage in long fiber epoxy composite laminates

A study of damage characterization of a GFRC laminate is presented here. Forty fatigue tests were executed and S–N curves traced. Two parameters were chosen to monitor damage evolution during each test: stiffness and dissipated energy per cycle. Moreover, the presence of three zones in graphs of processed data can be observed and it is evident that the most important structural transformations take place only in the very final part of life. Adopting a continuum mechanics approach, the degradation through the whole life in composite is evaluated and it is shown that the two parameters are strictly related to damage state of composite material. A method for predicting the remaining life in a GFRC is here proposed.     

A fatigue model for sensitive materials to non-proportional loadings

The present study proposes a novel fatigue model based on virtual strain energy. This model separates loading paths based on their non-proportionality where directly takes into account the loading in fatigue life prediction. The proposed fatigue model is expressed in two tension-based and shear-based equations for two tensile and shear cracking failure modes. The model was validated against several experimental datasets available in the literature. In addition, obtained results were compared to predicted lives through some well-known fatigue models comprising maximum shear strain, Smith–Watson–Topper, and Fatemi–Socie. The results were strongly correlated with the experimental data indicating accuracy of the model.     

A composite ply failure model based on continuum damage mechanics

A material model including the failure behaviour is derived for a thin unidirectional (UD) composite ply. The model is derived within a thermodynamic framework and the failure behaviour is modelled using continuum damage mechanics. The following features describe the model: (i) The ply is assumed to be in a plane state of stress. (ii) Three damage variables associated with the stress in the fibre-, transverse and shear directions, respectively, are used. (iii) The plastic behaviour of the matrix material is modelled. (iv) The difference in the material response in tensile and compressive loading is modelled. (v) Rate dependent behavior of plasticity and damage (i.e. strength) is modelled.     

Application of a material fatigue damage model in 4PB tests

The fatigue property of an asphalt mix is an important issue in pavement design. This property is often determined with the aid of a four-point bending (4PB) test in controlled deflection mode. The fatigue property is related to the decrease in the calculated complex stiffness modulus, however, due to the non- homogenous stress and strain field in the beam, the measured response does not represent the stiffness modulus of the material but a weighted stiffness value. For a correct interpretation, a fatigue damage material model like the Asphalt Concrete Pavement-Fatigue model is needed. After integration, the calculated and measured responses are compared. By varying the model parameters, an excellent comparison between the two responses is obtained up to a certain number of cycles. This number of cycles is denoted as the fatigue life N _PH . The accumulated dissipated energy at the surface of the beam in the midsection can be expressed as a constant times the fatigue life N _PH to the power z and also as a constant times the product of the fatigue life N _PH and the initial dissipated energy in the first cycle. Using these two findings, a Wöhler curve was established similar to the one directly based on the strain amplitudes and fatigue life data.     

Evaluation of the residual strength degradation in composite laminates under fatigue loading

Residual strength degradation in graphite/epoxy composite laminates is evaluated and a model proposed relating the residual strength to the applied fatigue cycles and the maximum applied stress. Based on this model, the statistical distribution of the residual strength is derived and compared with available experimental data. Good agreement is observed between the proposed model and experimental results.     

A new damage model for composite laminates

Aircraft composite structures must have high stiffness and strength with low weight, which can guarantee the increase of the pay-load for airplanes without losing airworthiness. However, the mechanical behavior of composite laminates is very complex due the inherent anisotropy and heterogeneity. Many researchers have developed different failure progressive analyses and damage models in order to predict the complex failure mechanisms. This work presents a damage model and progressive failure analysis that requires simple experimental tests and that achieves good accuracy. Firstly, the paper explains damage initiation and propagation criteria and a procedure to identify the material parameters. In the second stage, the model was implemented as a UMAT (User Material Subroutine), which is linked to finite element software, ABAQUS™, in order to predict the composite structures behavior. Afterwards, some case studies, mainly off-axis coupons under tensile or compression loads, with different types of stacking sequence were analyzed using the proposed material model. Finally, the computational results were compared to the experimental results, verifying the capability of the damage model in order to predict the composite structure behavior.     

Computationally efficient modelling of the fatigue behaviour of composite materials

Fatigue of composite structures is a complex process involving several types of failure. Existing approaches either neglect this complexity or require large computational effort. In this work, a simple progressive damage model including strength and stiffness degradation is implemented into finite element (FE) software. To reduce computational time, the major part of stress calculations is carried out by classical lamination theory. At single points of time, FE analysis is employed to support these calculations. The simplified model is tested against a reference model using FEA after each load cycle. Calculations are set up for a tensile specimen and a cap profile with quasi-isotropic layup. The simplified model using CLT is shown to be in good agreement with the reference while significantly reducing computational time.     

A combined elastoplastic damage model for progressive failure analysis of composite materials and structures

The paper is concerned with the development and verification of a combined elastoplastic damage model for the progressive failure analysis of composite materials and structures. The model accounts for the irreversible strains caused by plasticity effects and material properties degradation due to the damage initiation and development. The strain-driven implicit integration procedure is developed using equations of continuum damage mechanics, plasticity theory and includes the return mapping algorithm. A tangent operator consistent with the integration procedure is derived to ensure a computational efficiency of the Newton–Raphson method in the finite element analysis. The algorithm is implemented in Abaqus as a user-defined subroutine. The efficiency of the constitutive model and computational procedure is demonstrated using the analysis of the progressive failure of composite laminates containing through holes and subjected to in-plane uniaxial tensile loading. It has been shown that the predicted results agree well with the experimental data reported in the literature.     

A continuum damage model for asphalt cement and asphalt mastic fatigue

An analytical model is developed for the mechanical degradation of asphalt cement and mastic under repeated loading. The model is derived by applying the strain decomposition principle to consider linear viscoelastic, nonlinear viscoelastic, and damage mechanisms. The experimental processes to isolate the behaviors and the analytical functions used to model each are described. It is found that the Schapery type damage approach is capable of modeling the fatigue process of these materials once appropriate consideration is taken for their nonlinear viscoelastic responses. Fatigue in asphalt mastics is also found to occur due to physical damage occurring in the asphalt cement.     

Modelling fatigue crack propagation of a cracked metallic member reinforced by composite patches

The concept of fracture for material elements at front of a crack for fatigue crack propagation was extended to the fatigue crack propagation of a cracked metallic member reinforced with a composite patch in this paper. From static mechanics and linear elastic fracture mechanics, force transfer on a cracked member through a composite patch was analyzed and a formula connecting the stress intensity factor with crack length was obtained. Thereafter, a fracture model for fatigue crack propagation of a repaired cracked metallic member was proposed. A new expression for the fatigue crack propagation rate has thus been derived. The expression was verified objectively by the test data. It is in good agreement with the test results.     

A modified model for the estimation of fatigue life derived from random vibration theory

When a component is subjected to variable-amplitude loading, if the fundamental stress–life cycle relationship and an accumulation rule are given, then the fatigue damage or fatigue life of the component can be calculated and/or estimated. In the present paper, random vibration theory is incorporated into the analysis of the above problem. Several formulas are thus derived. Experimental work is then carried out to verify the derived formulas. Comparison is made among the results calculated based on different formulas, different accumulation rules and different random loading. It is concluded that the derived formulas do provide us with quick prediction of the fatigue damage or fatigue life when a component is subjected to variable-amplitude loading that has a certain random nature.     

An accumulation damage model for fatigue fracture of ferroelectric ceramics

The accumulated plastic displacement criterion for crack propagation in traditional materials is extended to develop equations to predict the fatigue crack growth of ferroelectric ceramics subjected to combined electromechanical loads. The crack-line is perpendicular to the poling direction of the medium. An electric saturation zone and a stress saturation zone are assumed to develop at the crack tips when the medium is subjected to external electromechanical loads. This assumption makes it possible to obtain the accumulated plastic deformation in closed form. A fatigue crack growth law, which is a fourth-power function of the effective stress intensity factor, similar to the well-known Paris law, is derived. Graphical results for the effect of electric load on the effective crack tip stress intensity factor and crack growth rate are provided.     

A micromechanics model for the prediction of fatigue characteristics of off-axis unidirectional laminates

In this paper, the concentric cylinders model is used to predict the fatigue characteristics of off-axis unidirectional laminates. A failure criterion that uses stresses averaged along the radial distance in each constituent phase is applied to predict the S-N curves of unidirectional laminates. The predicted S-N curves compare well with the experimental data for various off-axis Glass/Epoxy laminates.     

A strain energy based damage model for fatigue crack initiation and growth

A strain energy based fatigue damage model is proposed which uses the strain energy from applied loads and the strain energy of dislocations to calculate stress-life, strain-life, and fatigue crack growth rates. Stress ratio effects intrinsic to the model are discussed, and parameterized in terms of the Walker equivalent stress and a fatigue crack growth driving force. The method is then validated using a variety of different metals with strain-life data and fatigue crack growth rate data available on the SAE Fatigue Design & Evaluation subcommittee database.     

Assessment of fatigue damage evolution in woven composite materials using infra-red techniques

Thermoelastic stress analysis (TSA) is used to study the growth of fatigue damage in single and two ply, 2 × 2 twill woven composite materials. Test specimens were subjected to a uniaxial tensile cyclic loading with maximum stresses of 10%, 15% and 20% of the ultimate failure stress. The development of fatigue damage locally within the weft yarns is monitored using high resolution TSA. The specimens were subsequently inspected using optical microscopy to evaluate the location and extent of cracks. Cracks were found in the weft fibres, running transverse to the loading direction. It is demonstrated that the lighter weight fabric is more resilient to damage progression. A signature pattern is identified in the TSA phase data that indicates the onset and presence of fatigue damage in the composite material.