The increasing focus on reducing greenhouse gas emissions has led to the attractiveness of offshore hydrogen pipelines in achieving sustainable energy goals. Hydrogen, as a transport medium for energy, offers a viable alternative for transmitting large amounts of energy from offshore facilities to the shore. By storing hydrogen and subsequently converting it back into electricity during periods of peak demand, this approach aligns with the goal of establishing a green, net-zero economy by 2050. However, maritime activities in the proximity of offshore pipelines introduce a serious risk of damaging pipelines by accidental or emergency anchoring scenarios. Damage from dropped or dragged anchors can displace and harm pipelines, leading to environmental risks, safety hazards, and costly repair operations. Comparing hydrogen pipelines to existing oil and gas pipelines, there are significant differences. While oil leakage from anchor hooking poses risks to the environment and marine ecosystems, hydrogen imposes new risk factors which must be taken into account. Hydrogen negatively affects the structural integrity of pipelines, and anchor hooking leads to elevated stress levels within the pipeline material, accelerating fatigue crack growth, and reducing the operational lifespan of the pipeline. This leads to the following research question: ”What is the post-hooking lifetime of a hydrogen pipeline damaged by an anchor?”

To address this research question, the methodology applied in this thesis consists of two main approaches: numerical simulations and a fatigue crack growth model. The simulations specifically consider an incident where an 8-inch pipeline was damaged by an AC-14 High Holding Power (HHP) anchor. The pipeline is internally pressurised at maximum gauge pressure, and simulations are conducted considering daily and yearly variations in loading cycles, specifically at 10% and 50% pressure reductions. Through these simulations, the stress distribution and variation within the pipeline material resulting from the anchor impact are investigated, providing insights into the behaviour of the pipeline under such conditions. The fatigue crack growth model used in this study is based on the Paris law, which describes the relationship between crack depth and the number of cycles required for crack propagation under cyclic loading conditions. The presence of hydrogen significantly accelerates the rate of fatigue crack growth. As a result, adjustments are made to the Paris law to account for this effect, particularly in determining the range in which the law remains applicable. The crack growth analysis focuses on determining a critical crack depth, which could possibly lead to pipeline failure. A Failure Assessment Diagram (FAD) is used to determine the maximum allowable crack size, ensuring the safety of the pipeline. The FAD, along with the wall thickness of the pipeline, serves as a critical criterion for assessing structural integrity. The remaining lifetime of the pipeline following an accident depends on which criterion, either the FAD or the wall thickness, indicates failure first.

The crack growth analysis conducted in this research reveals that as the crack depth progresses under the influence of hydrogen, it eventually reaches a critical depth that introduces a potential risk of pipeline failure. Specifically, when considering yearly pressure variations, the crack reaches this critical depth in slightly over 8 years. Although the attained crack depth at this point is not yet through-thickness, the crack growth rate experiences a significant increase after 8 years, ultimately resulting in a through-thickness crack 9 years after the initial impact. The findings of this study have significant implications for the future development and maintenance of offshore hydrogen pipelines. By understanding the consequences of anchor hooking incidents and their impact on the operational lifespan of hydrogen pipelines, this research contributes to the development of robust and resilient infrastructure for a sustainable energy future.

The increased consciousness of the negative impact of human-induced climate change has resulted in rapid developments within the offshore wind industry. With Wind Turbine Generators (WTGs) becoming increasingly larger and available shallow water sites becoming scarcer, new offshore wind solutions must be developed to accomplish the goals set by today’s policymakers. The new deep water sites available for offshore wind are not applicable for the current benchmark of monopiles and jack-up vessels. New state-of-the-art applications, such as Floating Offshore Wind (FOW), come into play in the global offshore wind market. To meet this demand, Heerema is developing installation methodologies for floating to floating installation applications. One of these methodologies is the RNA+ method (Rotor Nacelle Assembly + Tower), lifting a fully assembled WTG module in one lift from the vessel deck on top of its foundation to limit the number of critical lifts. Operability studies are required to examine whether such operation is feasible. As the FOW industry is the new kid on the block, little is known about FOW’s configuration and other influences. Therefore, this research aims to determine the effect of design parameters of the three key components of an offshore floating to floating installation on its operability. These key components are the WTG, floater, and installation vessel. For this research, the IEA 15 MW reference turbine with an altered tower, a Tension Leg Platform (TLP) provided by Intecsea, and Heerema’s Semi-Submersible Crane Vessel (SSCV) Sleipnir were used as WTG, floater, and installation vessel respectively.

A numerical base case model containing these key parameters was built to address the influence of the design parameters. This base case models the free-hanging stage of a complete WTG module suspended in the SSCV’s crane 3 m above the TLP in a water depth of 150 m. The numerical model was analyzed in the Frequency Domain (FD), considering only first-order effects. With respect to this base case, all parameter variations were compared. A mean JONSWAP spectrum was used as wave spectrum.

The results show that this installation method is sensitive to long wave periods ( > 8 s). The clearance between
the nacelle and crane-boom is deemed the most governing limiting criterion. The relative vertical Z-tip motion between the tower bottom and TLP top and the side-lead angle of the crane hoist wire are the secondary governing limits. Design parameters that influence the static clearance between the nacelle and crane-boom have the most impact on the total operability. With the current design parameters world’s largest SSCV has a limited operability for installing the modified version of the IEA 15 MW reference turbine with a single crane lift. Alterations to increase its crane boom reach and clearance are needed to perform this single lift installation. The hub height and nacelle casing size of the WTG limit the operability significantly. Furthermore, due to its relatively small size, stability and stiffness in heave direction, the TLP hardly affected the operability.

Accelerated tests have been commonly used by the marine coating industry to evaluate the performance of a coating in a short duration of time. Replicating natural exposure in an artifi- cially simulated manner is a challenging task due to the various factors that induce corrosion in the natural environment. Continuous salt spray testing is a popular accelerated test, but it does not replicate the actual exposure scenario as intensifying the factors inducing corrosion does not produce the same result as natural exposure. However, it was found that alternating between wetting and drying of the coating correlates well with natural exposure. ISO 12944- 9, a standardized accelerated test for corrosion protection in the marine environment, is one such test which alternates between different exposure conditions. This is performed in order to replicate the exposure conditions that a marine structure experiences. This ultimately aids in understanding the performance and durability of the coating within a shorter period. Besides, accelerated tests can be used to correlate with the natural exposure, in order to circumvent the issue of testing coatings in the natural environment for years to understand the coatings performance and durability. This thesis aims to correlate the performance of a commercial marine vinylester coating re- inforced with glass platelets named Ecospeed, when exposed in a natural service life envi- ronment versus that when tested in an accelerated environment. For accelerated ageing, the standard ISO 12944-9 was used, which is the standard exposure conditions for coating sys- tems undergoing extreme conditions in the marine environment. For the natural exposure, two in-service vessels coated with Ecospeed were selected to test its performance. Both vessels were coated with Ecospeed for 10 and 15 years. The coating’s performance is evaluated using electrochemical impedance spectroscopy (EIS) in both the natural and accelerated environments. EIS measurements were performed at peri- odic intervals of 1000 hours until 3000 hours for the accelerated exposure. EIS measurements were obtained on the 10 and 15 years old ship at multiple locations on the hull. This was done to check the uniformity of corrosion protection and variation of coating performance across the ship. Pull-off adhesion tests were also conducted after 2000 hours of accelerated exposure and the strength was reduced to more than half its initial strength prior to exposure in ISO 12944-9. The results of the accelerated test indicated gradual reduction in the impedance of the coating over 3000 hours of accelerated test exposure. The magnitude of impedance at the lowest frequency of 10 ́1 Hz was 4.23 x 1010 Ω cm2 after 3000 hours of accelerated exposure and for the 15 year field exposure the magnitude of impedance was 4.27 x 109 Ω cm2, which is well above the minimum industry standard of 107Ω cm2. Considering the impedance values for both the accelerated and natural exposure, it can be said that the impedance of Ecospeed is atleast 2 orders of magnitude higher than the minimum industry standard requirement even after 15 years of natural exposure. The accelerated results of 1000 hours had good correlation with the impedance measurements performed on the 10 year old ship. The magnitude of impedance of the 15 year old ship was lower than the magnitude of impedance obtained from 2000 and 3000 hours of accelerated exposure. This means further exposure in the accelerated environment is needed to correlate with a 15 year old ship.

After decades of exploitation of hydrocarbons, the offshore facilities constructed for this purpose are nearing the end of their design life and/or economic operation. According to international law, these offshore structures need to be completely removed. Decommissioning of the substructures often requires for soil to be removed in piles to facilitate pile cutting works below the seabed. One way of achieving this is by deploying a specialized tool, a so-called Soil Plug Removal Tool (SPRT), that operates using hydraulic excavation.

This research carried out under supervision of Royal Boskalis Westminster N.V. aims to get a more solid basis for comparison of different SPRT concepts that are available in the market. The tools are designed to handle a wide range of soil types. Removal of cohesive sediment is more challenging, mainly due to the very low water permeability present compared to granular soils. This study therefore focusses on the excavation of cohesive soil types only.
In order to verify the performance of several concepts an experimental test program is set up on model scale. The primary goal is to investigate the achievable excavation production in terms of tool progress rate. Therefore, a jetting tool is developed that covers the (complete) spectrum in terms of cohesive soils and performance of the available tools. Two basic SPRT concepts are incorporated in this single tool based on head movement: static or rotating.

Jet pressure, clay strength, rotational velocity and set down pressure of the tool are altered during testing on the condition that all other parameters are fixed. This requirement is met for the testing clay by merely varying the shear strength. The testing clay was therefore prepared both with an artificial and natural clay with shear strengths ranging from 20 kPa to 100 kPa.

It is found that next to jetting, soil failure can also be attributed to cutting and jet trench failure under influence of the jetting head that rests on top of the clay. For this reason, production values belonging to jetting could not be obtained directly and had to be calculated using jetting theory to distinguish between jetting and jet trench failure. Based on the power that is required to excavate a certain volume of soil (i.e. specific energy), insight is given in the contribution of each failure mechanisms to the production in terms of tool progress rate.

During static jetting, the current (nozzle) configuration did not remove enough soil from the jet cavities for the jetting tool to progress downwards. The opposite is true for the rotational tests which comprise the largest part of the test series. An analytical model is proposed to predict the cavity width and depth. This model is only valid for jets with small rotational velocities as encountered in this study.

The total production, which was measured, is found to be inversely proportional to shear strength and directly proportional to jet pressure and rotational velocity.

Over the last two decades, the size and capacity of (container) vessels calling port at the Port of Rotterdam have increased considerably. To moor these huge and heavy ships safely at the quay, fenders are frequently installed. The present guidelines for the “Design of Fender Systems”, which were established in 2002, are due to be updated in 2023. Part of the update of these new guidelines for the design of fenders by working group 211 of the Permanent International Commission for Navigation congresses (PIANC) consists of the verification and validation of the hull pressure criterion, taking into account the recent growth of (container) vessels. Obtaining a generic criterion is challenging due to the enormous diversity in vessel sizes and structural layouts. In addition, fender dimensions and types may also have a significant influence on the fender-induced load. This leads to the following research question: “How can critical fender-induced loads acting on the parallel side hull be quantified, accounting for the diversity of vessels and fenders?”

In this research, parallel hull sections are used in numerical simulations to investigate the allowable load of fenders and to derive the influence of panel size and dimensions (tall or wide). Including detailed parallel hull sections for a representative group of vessels, makes it possible to look beyond simplified geometries, such as stiffened panels, and specific case studies. First, the structural response and corresponding governing failure modes were studied. In addition to existing failure modes described in fender-induced loads, tripping of stiffeners as a possible governing failure mode was included. A modification to available analytical formulations was made to describe the critical tripping pressure of stiffeners with a flange under patch loads more accurately. The proposed critical tripping pressure induced by a fender is underestimated by the analytical model in comparison to the numerical simulations of the parallel sections. When the rotational restraint of the web frame attached to the tripping stiffener is considered, a closer correlation between the analytical results and the numerical simulations of the parallel hull is foreseen. For the numerical simulations, a parametric approach was adopted, where different impact locations and contact areas were applied for several vessel types and sizes. The lowest steel grade of vessels currently applied in shipbuilding was implemented to obtain the lower limit of allowable fender-induced loads.

The key finding of this study is that allowable fender-induced loads are largely influenced by the vessel's structural dimensions, such as web frame spacing, and the size of the fender panel with respect to the ship's geometry. The constant hull pressure criterion currently used by PIANC can be maintained but should be limited to a total allowable reaction force, because, for large panels, it overestimates the capacity. Furthermore, it has been shown that for large ships, wide panels outperform tall panels because they activate web frame(s). Making panels much wider does not necessarily yield more capacity because the stress concentration remains in the web frames. For small vessels, the trend is less clear, as the web frame is activated at an earlier stage (less far apart) and the capacity does not increase exponentially with the width. In addition, high panels on small vessels sometimes lead to the activation of a deck and thus increase the allowable load. The overall conclusion of this research is that the PIANC criterion should be limited to a total reaction force. Furthermore, by correctly sizing fender panels, more efficient use of the vessel's capacity can be ensured, as web frames provide more capacity. The findings of this research can be used to allow small and large vessels to safely berth onto existing facilities.

Increasing competition amongst airlines necessitates them to improve the efficiency of their operations. Even though maintenance, repair, and overhaul (MRO) represent a significant portion of an airline’s operational costs, aircraft maintenance scheduling is often still a manual process, producing suboptimal solutions. Airlines typically operate by congregating the bulk of the required maintenance tasks in extensive checks, called letter checks (A, B, C, or D). Letter checks require the aircraft to be taken out of operations and result in many tasks being executed before they are due, leading to more required maintenance over the aircraft's lifetime. The purpose of this study is to develop a methodology that provides flight routes to aircraft and plans the maintenance tasks individually within these routes over a given planning horizon with the objective of maximizing the utilization of the total remaining flying time of the fleet. To achieve this, tasks are planned as late as possible on overlays at a maintenance station, while being given a due date and a remaining number of legal flight hours that can be flown before execution is mandatory. For this purpose, we develop a mixed integer programming (MIP) model based on a city-day network representation. Because the computational burden of exact methods becomes too hefty for increasing problem sizes, several matheuristics have been developed to provide good solutions in quick fashion. The presented matheuristics either decompose the problem by aircraft or into time periods. The former constructs the flight routes and maintenance schedules aircraft per aircraft while the latter constructs them simultaneously in a rolling horizon fashion. For the rolling horizon matheuristics, several forecasting strategies have been designed as well. In an experimental study, one of the selected rolling horizon matheuristics was able to remove the need for aircraft to be taken out of operations for an A-check (the most frequently occurring letter-check), potentially saving up to \$ 7.2 million per aircraft over a time period of ten years. Furthermore, the lost flying time, incurred by planning maintenance tasks before they are due, was decreased by over 98\%, resulting in a higher utilization of the task intervals and less required maintenance over the aircraft's lifetime. Finally, the dissection of the A-check into its individual tasks led to a more phased maintenance schedule by attenuating the peaks in workload for the mechanics workforce. Our presented approach can be used by mid-sized airlines to optimize their maintenance schedules through increasing aircraft availability and reducing maintenance costs over the aircraft's lifetime.

A fairly recent development in the maritime industry is the rising interest in composites, as they have great potential to outperform conventional metallics. They offer good corrosion resistance, fatigue resistance, a low magnetic signature, and a high strength to stiffness ratio. In case of a propeller, the latter may be utilized by adapting the geometry passively to suit the loading condition more optimal. A possible is to mitigate cavitation by utilizing the relatively large deformations when subjected to loads. The hydrodynamic response of a flexible propeller in a flow field can be predicted by the use of Fluid-Structure Interaction (FSI) software, which is currently being developed at MARIN. The project is called ComPropApp, and combines existing fluid and structural solvers. As the ComPropApp is still under development it needed to be verified and validated, which is the main objective of this thesis. As an initial step in the verificatio, a falsification study was applied on the procedures followed in the ComPropApp. This led to the discovery of several errors, to which corrections have been applied to improve the program. With an updated version, computations with a number of different materials were performed to finalize the verification. Then, a model size polyurethane propeller has been manufactured at MARIN to be used in the experimental validation. Experiments were performed in the cavitation tunnel testing facility at MARIN. Here the propeller was tested in several operating conditions, which was then compared with ComPropApp simulations. Lastly, it was investigated whether the application of a composite can reduce cavitation. This was for theoretical research only, since the testing propeller would fail far before reaching cavitating conditions. With the fluid solver, a requirement for twist deformation was set up. Based on these requirements, a range of composite materials was defined, and with it, ComPropApp computations were performed. The resulting displacements and pressure distributions were then compared for rigid and composite propellers. With the presented verification study, it can be concluded that the FSI software is capable of providing realistic computation results. The validation study has led to conclude that the unsteady FSI module is capable of qualitatively predicting the bend deformations in open water conditions. However, due to the large uncertainties arising from the testing material properties and questionable machining quality, the measurements cannot be utilized to define the accuracy of the FSI software. In wakefield conditions the additional uncertainty of the wake velocity distribution meant that these measurements are inconclusive, hence the validation was only performed for open water conditions. The material study with the purpose of mitigating cavitation has shown potential in the application of anisotropic materials. Composites with a specific ply orientation sequence have the possibility of realizing bend twist coupling motions, such that the propeller would unload itself in the vicinity of the ship hull, with reduced cavitation as an expected result.

This work comprises research in the field of Experimental Dynamics. This technique is currently used in the automotive area and is used to enhances the current state of FEM with the inclusive of test- based models. Building test-based models for EDS (Experimental Dynamic Substructuring) requires very accurate measurement, and this thesis examines how uncertainty on sensors and impacts affects the accuracy of the test-based model. Dynamic Substructuring is the collection of methods to describe large and complex systems by using the models of its substructures. This approach assumes that the dynamics of each substructure is enclosed in a so-called super element at interface DoF. Modeling domains that engage condensed dynamic information, like admittance FRFs in the frequency domain, are therefore particularly suited for substructuring [49]. One of the methods to model the interface between two (or more) substructures, is coupling two sub- structure by a single mutual point, so-called Virtual Point. This single point is a collocated point, a super-element, which has both translational and rotational DoFs., In order to obtain the FRF of the coupling point of each substructure, an experimentally gained in- formation is transforming into the super-element’s admittance (Virtual Point FRF). The experimentally gained information is recorded by sensors and roving impacts. The transformation uses projection ma- trices for both input and output and is called Virtual Points Transformation (VPT). In all experiments, we almost always have some uncertainties, and achieving true experiments is al- most impossible. Making errors while mounting the sensors and roving impacts is very plausible. This mounting errors can be positional as well as directional. Because of these uncertainties, we can never find the true transformation matrices. In this thesis, the propagation of the positional and directional uncertainty of measuring equipment (sen- sors and roving impacts) into the calculation of Virtual Point frequency response function is investigated analytically, as well as numerically. It is shown which error and in what extend is the most dominant er- ror source, and in which frequencies and in which cross-functions of V P we can expect the least precise. Expectations can be made on the inputs’ or outputs’ DOF with dominant effect on error generation for a particular mode shape, based on the local mode shape-motion of measurement area, and by using the Component Mode Synthesized method (CMS). It is shown that the error generation on measurement, and further error propagation into super-element caused by a particular error source is mode shape- and frequency-dependent. Further, an estimation is given for the amount of influence of each dominant error source on the cal- culation of the forces and responses of Virtual Point, on both rotational and translational forces and responses. Since the dominant error generation is depending on the mode shape motion, the V P’s cross-functions with the least precision can also be defined.
It is shown that based on the decomposition of transformation matrices, the rotational/ rotational cross- functions are the most sensitive ones to both positional and directional uncertainties if we are looking to absolute value. Then, base on the numerical results, a comparison is made between all four studied cases; Impacts Positional Uncertainty (IPU), Impacts Directional Uncertainty (IDU), Sensors Positional Uncertainty (SPU), and Sensors Directional Uncertainty (SDU). The possibility of error cancellation and the maximum error propagation is introduced.

Strain rate, how fast a material is strained, is known to have an effect on the behaviour of metals. Being able to measure the effect of strain rate in a material provides more reliable material data as input for material models. Strain rates up to 10 per second can be tested using a (fast) hydraulic testing machine. Strain rates upwards from 500 per second can be tested using a Split-Hopkinson bar, but for the strain rates in between no such standard method is available. The goal of this thesis is to provide a design guide for a reliable experiment that measures the effect of strain rate, in the range 10-100 per second, on the tensile stress-strain curve of a metal. The test method proposed in this thesis consists of two parts. The first part is a test using a universal testing machine to determine material behaviour at low strain rates of 0.001-10 per second. A regular dogbone specimen with a longer grip section is used for the UTM tests, which provides the material data to design specimens for the second part. The second part is an impact test where a drophead impacts a specimen, causing it to strain. The specimens are U-shaped strips with a dogbone at either side to test material behaviour at higher strain rates of 10-100 per second. For both tests, strains are recorded in the grip and gauge sections by means of a DIC system. The main advantages of the proposed test method are (i) that no sensors are required in the drophead as the load is extracted from strain measurements in the linear elastic grip section, while the gauge section is allowed to deform plastically and (ii) by using DIC, unobtrusive measurements are taken of the strain field in the recorded area. Two analytical models have been developed, one for the universal testing machine tests and one for the impact tests. The analytical models for the UTM tests and the impact tests have been compared to a finite element model of the same specimen. When plastic strain in the gauge section becomes the most dominant component of the strain, both analytical and FE strain curves show good agreement. Numerical simulations of the impact test have been done by means of an explicit, dynamic, non-linear impact simulation using finite element analysis. A parametric study has been done using the FE model to determine the effect of drophead mass, impact velocity and specimen dimensions on the strain rate in the gauge section and the measurement accuracy. Based on the results of this study, a guideline is presented for performing the experiment. In conclusion, a novel test method and corresponding guideline to determine the stress-strain curve of metals at intermediate strain rates in the range of 10-100 per second has been presented and demonstrated by means of numerical simulations. As a future step, a set of experiments should be performed to prove the validity of the proposed test method.

Viscoelasticity is a material property that is relevant in a variety of nanoscale materials and interfaces in medicine and industry. Therefore, a method of mechanical quantification has become exceedingly desired. In this thesis the Atomic force microscope (AFM) is applied to accurately characterize the mechanical behavior of viscoelastic samples. The goal is to enhance viscoelastic characterization using the so-called Intermodulation AFM (ImAFM) technique by applying, adapting and improving multiple modelling and optimization methods. In ImAFM force reconstruction is performed by extracting intermodulations around resonance in the cantilever response. These intermodulations present new observables that can be used for characterization. This thesis investigates the potential of this technique in combination with an up-and-coming model describing viscoelastic interaction. A toolbox has been developed for numerical simulations of the model to resemble the experiments. The model has been evaluated in a variety of situations using sensitivity analysis in a large feasibility range, encompassing many complex dynamics. Because of the diversity in model dynamics a global optimization has been performed for experimental reconstruction.

The stay cables of the north bridge of the Galecopperbrug are reaching the end of their life span. Rijkswaterstaat, which is responsible for the bridges, needs a reliable Structural Health Monitoring (SHM) method to monitor the current state of the stay cables. At the moment, Rijkswaterstaat experiences issues with defining the state and the residual life span of the stay cables of the
Galecopperbrug. This study focuses on the technique of Acoustic Emission (AE) for monitoring the stay cables of the Galecopperbrug. The main research question of this study was: “Is the AE-system used in a fracture-based assessment suitable for structural health monitoring of the stay cables of the Galecopperbrug?”. In this study the following methods were used to investigate the AE behaviour of stay cables: a literature study on previous research and the current knowledge of AE and the structural behaviour of cables was done, a full-scale and two verification experiments were performed to investigate the AE behaviour related to wire breaks and to investigate the accuracy of linear source location techniques, an analytical model of the stay cables was made to investigate the influence of different parameters to the capacity of the stay cables and to predict the stress distribution in the wires during the experiment and finally, a SCIA model of the Galecopperbrug was used to investigate the load bearing distribution of the Galecopperbrug. In this study, it was found that wire breaks inside (stay) cables will generate elastic stress waves which can be captured and recorded by AE sensors. Based on an experiment where multiple wire breaks occurred, it was shown that wire breaks can be identified with the help of AE techniques. However, the identification of wire breaks is mainly depending on the correct choice of sensor type. Based on the experiments and assumptions that were made in this study the R6I-AST type of sensors are more suitable for wire break detection and the R3I-AST sensors are more suitable for AE signals due to impacts. Based on the assumptions and the experiments performed in this study it can be concluded that AE can be used in a fracture-based assessment for SHM of the stay cables of the Galecopperbrug.

In order to monitor elliptical fatigue crack growth in ferromagnetic steel using magnetic methods, analternative to the self magnetic flux leakage method must be derived as elliptical cracks can grow to significant sizes before they reach through the thickness of the plate material. An approach is sought by translating subtle changes in magnetisation back to the Villari effect, a phenomenon which depicts how applied stress induces changes in magnetisation in ferromagnetic objects. Since the magnitude of these changes in magnetisation is small, other nonlinear effects of similar order such as magnetic relaxation and hysteresis are identified, measured and quantified preliminarily.

The magnetic behaviour in this project is assumed to be quasi-static, and derivations of the expressions for the magnetic field around simple geometric shapes are provided in order to understand magnetic behaviour and verify the outcome of the numerical simulations. It is shown that the numerical simulations
produce identical magnetostatic induction fields as the analytically derived expressions when using a sufficiently refined mesh.

An attempt is made to measure long-term magnetic relaxation by subjecting a solid prolate spheroid to a continuous uniform background field for periods of an hour while trying to measure differences in the induction field at a fixed distance. Short-term relaxation, the time it takes for an object to reach a certain
magnetisation when the background field is abruptly changed, is also investigated. It is concluded that both effects could not be successfully measured using the current setup. In order to draw proper conclusions, further research into this topic should be conducted using more accurate equipment for extended periods of time.

Upon investigation it is discovered that it can not be assumed that the steel specimens exhibit a uniform permanent magnetisation. A self-developed method is introduced through which non-uniform magnetisation in three directions can be calculated by means of inversion using a set of magnetic induction field measurements in a plane below the specimen when the background field is zero. These measurements are translated to magnetisation using a set of higher order square Gaussian distribution functions that are spaced in a grid over the domain of the test specimen in order to vary the magnetisation locally.

Literature that shows comparable results regarding description of non-uniform permanent magnetisation using an array of induction field measurements has not been found. The concept of hysteresis is introduced and a method is presented through which the parameters of the Jiles-Atherton hysteresis model can be determined using parameter fitting in combination with a forward numerical model created in COMSOL. Closure of minor loops require modifications to the original JA equations which are implemented in the forward model. The numerical model is encapsulated within the Shuffled Leaping Frog parameter optimisation algorithm in order to compute the correct hysteresis
parameters. It is found that it is possible to successfully determine the parameters of multiple specimens using weak magnetic fields, and therefore minor loops, which is unparalleled in literature.

Eventually, the Villari effect is introduced and an attempt is made to measure and model the effect usingan extension of the Jiles-Atherton model proposed by Naus. Experiments have shown that using this methodology the magnetostriction parameters can be succesfully obtained. A recommendation is
provided into how these results can be implemented in crack-propagation models in future research.