A Probabilistic SCG Model for Transverse Cracking in CFRP Cross-ply Laminates under Cyclic Loading

A probabilistic static fatigue model for transverse cracking in CFRP cross-ply laminates

The stiffness reduction as a result of multiple transverse cracking in cross-ply laminates and the crack density dependence on the applied tensile stress are analyzed by linear elastic fracture mechanics. The stress field distribution is obtained by the principle of minimum complementary energy. Two models are suggested which describe the non-uniform stress distribution in the thickness direction of the 0° layer. They contain the variational approach presented by Hashin as a particular case. Elastic ply properties and the Mode I critical strain energy release rate GIc for transverse cracking are the experimental data needed. Model predictions are compared with experimental data for glass fiber/epoxy, AS4/3502, and AS/3501-06 carbon fiber/epoxy cross-ply laminates. The predictions from the suggested models describe both the constraint effect and the crack saturation phenomenon.

This paper investigates the effect of transverse cracks on the S0 mode velocity in GFRP and CFRP cross-ply laminates, and proposes a new AE source location method that considers the change in the S0 mode velocity due to the transverse cracks. We found experimentally that the stiffness and the velocity decreased as the transverse crack density increased. Analytical predictions deduced from the combination of the complete parabolic shear-lag analysis, the classical plate theory and the laminated plate theory are in good agreement with the experimental results. Utilizing this relationship between the velocity and the mechanical damage, we located AE sources of transverse cracks in cross-ply laminates with the calculated in situ velocity. We were able to show that highly accurate source location requires the reduction of the in situ value of the velocity. The present method is simple but quantitative and useful in health-monitoring for detecting and localizing the damage in composite structures.

FBG-based real-time evaluation of transverse cracking in cross-ply laminates

Cohesive modeling of transverse cracking in laminates under in-plane loading with a single layer of elements per ply

Transverse cracks in cross-ply laminates are investigated experimentally to reveal the essential characteristics of their opening displacement under tensile loads. The average crack opening displacement is studied as a function of the longitudinal overall strain and the effects of matrix toughness and transverse ply thickness on this parameter are examined. The interactive effects between closely spaced transverse cracks are also ex amined and found to be significant. Implications of the experimentally observed features on the micromechanics and continuum damage type models are discussed.

From the results of stress analysis between two transverse cracks in cross-ply laminate [1], a model for the stiffness reduction based on generalized plane strain assumptions has been developed. Simple analytical expressions are obtained for the longitudinal modulus and the Poisson's ratio as a function of the transverse crack density. Apart from the crack density, these expressions depend only on the elastic and geometrical properties of constituent laminae and the average crack opening displacement (ACOD) normalized in the proper way. Calculations of the ACOD are performed and analyzed with the FEM and analytical models used for the stress analysis in [1]. The predicting capabilities of approximate models are discussed in comparison with experimental data and FEM results. In order to predict the stiffness degradation for a wide variety of laminates, a simple procedure requiring only one FEM calculation for some “average laminate” with “average crack spacing” is proposed and has been proved effective.

A numerical study of transverse cracking in cross-ply laminates by 3D finite fracture mechanics

A model to predict transverse cracking in cross-ply laminates in the presence of residual thermal stresses is developed here. This model is based on the coupled criterion of the finite fracture mechanics. This criterion has been successfully used for different materials, structures and scales to predict crack initiation. It is based on two main hypotheses: (i) crack initiation occurs as a finite-length crack onset and (ii) the crack onset requires that both stress and energy criteria are fulfilled simultaneously. The present model is developed under the generalized-plane-strain hypotheses combining the results obtained using the laminate theory and a boundary element code. The present analysis shows that the residual thermal stresses affect both the stress and the energy criteria in the form of adding a residual elastic-strain to the strain imposed by external mechanical loads. An explicit expression for this residual elastic-strain is provided. For certain composite materials as carbon/epoxy the value of this residual elastic-strain is shown to be relatively large in comparison with the nominal critical transverse strain of the material. The comparison with experiments shows that considering the residual thermal stresses using the strategy proposed here improves drastically the accuracy of the model predictions.

A model is developed to predict the transverse crack density and strain response in a cross-ply laminate under monotonic, bilinear and constant loading. First, the strain response of the cross-ply laminate due to transverse cracking is presented based on the viscoelasticity theory and shear lag analysis. The transverse crack density is given as a function of both time and stress using a probabilistic failure concept. Secondly, monotonic tensile tests, bilinear tensile tests and constant load tests of cross-ply laminates are carried out to measure the strains and transverse crack density. A few parameters necessary for the probabilistic function are determined from the monotonic tensile tests at various stress rates. Finally, good agreement of strains and crack density in bilinear and constant load cases between experimental results and predictions verifies the validity of the present model.

Presented test results on transverse cracking in cross-ply laminates upon tension–tension cyclic loading show that the increase of crack density depends not only on the maximum transverse stress in the cycle but also on the local cyclic stress ratio RTloc in the analyzed layer. To include the effect of the RTloc in the model with statistical failure stress distribution for crack initiation (based on Weibull distribution) adapted for fatigue, an equivalent stress is introduced in a similar manner as the equivalent strain energy release rate has been used for delamination crack propagation. The equivalent stress in the layer is defined as a power function of the maximum stress and the stress ratio in the layer. It was found, testing laminates with two different fiber contents that higher the local stress ratio in 90-layer, higher the transverse cracking resistance. Transverse crack density simulation using the developed equivalent stress model has been validated against test results.

Development of transverse cracking in cross-ply laminates during fatigue tests

Modelling the transverse cracking in cross-ply laminates: application to fatigue

Chapter 3.4 - Predicting transverse crack formation in cross-ply laminates

This study deals with transverse cracking in cross-ply laminates. A fracture mechanics analysis, using a strain energy based criterion, was used to model the onset of transverse matrix cracking, and the conditions for further damage development. An admissible displacement field, involving unknown functions was assumed, and the principle of minimum potential energy was used to establish these functions. The crack front shape was a part of the assumed displacement field, thus making it possible to minimise the strain energy with respect to the crack opening displacement function. In this paper the aim was to establish a solution to the transverse cracking problem, to use later in a numerical procedure for the viscoelastic damage predictions for a cross-ply laminate. The model accounts for residual stresses. A number of finite element solutions were performed to verify the accuracy of the presented analytical solution. Predictions of stiffness degradation due to matrix cracking, and matrix cracking as a function of applied stress are presented.