Tunnelling cracks in composite laminates under planar biaxial strain controlled fatigue loading

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Predicting the life of a composite structure such as a wind turbine blade is not an easy task. This usually requires a multi-scale testing framework to specifically characterise the damage modes at different lengths scales and at the same time a multi-scale modelling framework that is mechanistic at its core. This is important as fatigue damage in com­posite laminates is multi-scale in nature. With this overarching goal in sight, this Ph.D. project studies the growth of tunnelling cracks under various biaxial loading conditions using a cruciform specimen and further builds a stochastic multi-scale damage model with mechanistic features which can have the potential to be applied to a structure. For the first time, crack density evolution plots from cruciform specimens are presented and also used to characterise a damage model. Further, it is of interest to investigate if a cruciform specimen can be the ideal coupon specimen in a multi-scale testing framework to recreate tunnelling cracks that may occur in structures under a realistic biaxial strain state.

This Ph.D. project is part of a larger research group consisting of three joint Ph.D. projects (CASMaT Initiation Project), which are aimed at studying multi-scale fatigue damage as a result of tunnelling cracks at the sub-structural, meso- and the micro- length scales. The work in this project is primarily concerned with the meso-scale.

Through extensive finite element analysis, the performance of various cruciform spec­imen designs are evaluated as a function of the anisotropy exhibited by multi-directional composite laminates. This is considered to be an important step towards standardising the cruciform specimen. It is seen that a single cruciform design for all material anisotropic configuration is not possible as the shape of the gauge zone, corners formed by the adjacent arms, the design of the arms, the layup configuration and the biaxial loading state largely affect the uniformity of the stress state in the gauge zone. However, candidate cruciform specimens are presented that perform well under most anisotropic configurations.

Two biaxial strain control algorithms are presented as fatigue testing strategies for cruciform specimens capable of tracking a strain state locally measured at the gauge zone of the specimen. This is important in a multi-scale testing framework as the locally measured biaxial strain state obtained from a structure may be utilised as an input to the biaxial cruciform specimen for recreating the damage. The two cyclic strain control algorithms, referred to here as the active and the passive control methods, use a real time digital image point tracking method to provide a contactless biaxial strain measurement, so that the gauge zone can provide an uninterrupted view of the damage evolution process. Even though both the methods use a strain-force coupling matrix for calculating the forces required to be applied to achieve a certain biaxial strain state, the active method is a cascade control architecture whereas the passive method is a conditional algorithm. For the passive method, the force command is adjusted when the measured peak-valley strain violates the pre-defined strain tolerance.

The relevance of the designed cruciform specimen and the strain-controlled testing method are evaluated using a multi-scale testing framework built with the other two Ph.D. projects involved in the CASMaT Initiation Project. Here, the crack density evolution measured locally from the gauge zone of a sub-structural beam under a multi-axial loading condition is compared with the observations from the gauge zone of a cruciform specimen, such that the strain state between two gauge zones are similar. Later the growth rate of non-interacting crack-fronts seen in the gauge zone of a cruciform specimen are compared with the observations from an equivalent uniaxial laminate such that the energy release rate and the mode-mixity of the crack-fronts are similar.

As a step towards building the multi-scale damage model, characterisation tests are conducted under uniaxial force and strain-controlled cyclic loading for the behaviour of interacting and non-interacting tunnelling cracks. A single strain-controlled cyclic test is found to be enough for producing a Paris-Erdogan type of law relating the crack-front growth rate with the energy release rate. However, force-controlled cyclic tests are still needed to characterise the stochastic nature associated with the growth of the tunnelling cracks at a constant steady-state energy release rate. Further, commonly seen interaction scenarios are identified where it is shown that a decrease in the volume averaged stresses between two closely placed cracks leads to a decrease in the growth of the crack-front belonging to a third crack growing in between them. Further, two complex interaction scenarios are studied. If the cracks are collinear and their crack fronts are growing towards each other for coalescence, it is found that the crack fronts do not influence each other. But, in a case when the two cracks are not collinear, the growth of crack-fronts are significantly affected after they grow past each other.

Finally, a multi-scale stochastic crack density evolution model is presented with the aim of making the model applicable to a structure. The damage model proposed in this work uses a stress based crack initiation criterion (local hydrostatic stresses and local maximum principal stresses) and a triple unit cell approach to predict the growth of cracks. Here, the GLOB-LOC model, that belongs to the class of crack face displacement models, is used to produce inputs to the crack growth model. Biaxial cruciform specimens and uniaxial rectangular specimens under strain and force-controlled cyclic loading respectively are used to calibrate the proposed damage model. The calibration includes development of the crack initiation SN curve, a Paris-Erdogan type of law for crack growth and the stochastic nature associated with both. The damage model is provided with a crack element discretisation scheme which allows for multiple collinear cracks to initiate and coalesce. The model calculates the energy release rate of individual crack-fronts explicitly based on the changing local cracking scenarios around the crack-fronts. The performance of the crack growth model is compared with 3D finite element analysis and experiments. The uniqueness of the model also lies in the consideration of damage outside the primary representative volume element (RVE) of the model. Finally, the performance of the crack density evolution model is compared with the experimental crack density observations from cruciform specimens.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages264
ISBN (Print)978-87-7475-650-7
Publication statusPublished - 2021
SeriesDCAMM Special Report


  • Composite Materials
  • Cruciform Specimen
  • Fatigue
  • Damage Modelling
  • Tun­nelling cracks
  • Biaxial Strain Control


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