Permeability (electromagnetism)

In electromagnetism, permeability is the measure of magnetization produced in a material in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter μ. It is the ratio of the magnetic induction B to the magnetizing field H as a function of the field H in a material. The term was coined by William Thomson, 1st Baron Kelvin in 1872, and used alongside permittivity by Oliver Heaviside in 1885. The reciprocal of permeability is magnetic reluctivity. In SI units, permeability is measured in henries per meter (H/m), or equivalently in newtons per ampere squared (N/A2). The permeability constant μ0, also known as the magnetic constant or the permeability of free space, is the proportionality between magnetic induction and magnetizing force when forming a magnetic field in a classical vacuum. A closely related property of materials is magnetic susceptibility, which is a dimensionless proportion

Visualisation of magnetic domain structures and magnetisation processes in Goss-oriented, high permeability steels using neutron grating interferometry

Benedikt Karl-Josef Gerhard Betz

Industrial transformers cores are built from stacked sheets of an iron silicon alloy, called laminations. The magnetic domain structures of these highly anisotropic electrical steels with a sharp (110)[001]-texture, the so-called Gosstexture, determines the magnetic properties of transformers. Commonly used investigation techniques for these laminations are inductive B-H-measurements. This technique reveals global magnetic properties such as hysteresis, remanence, saturation and losses. Locally resolved information about the underlying domain structure cannot be obtained. In this thesis, the neutron grating interferometer (nGI) is used to investigate the domain structures in Goss-oriented (GO) electrical steels at the Swiss Spallation Neutron Source using the cold neutron imaging facility ICON. In contrast to the attenuation based transmission image, the dark-field image (DFI) is related to multiple refraction of unpolarised neutrons at magnetic domain walls. Thereby the use of the DFI allows for the visualisation of bulk magnetic domain structures in two and three dimensions with a spatial resolution of down to 70 um in a field of view of 64mm x 64mm. The DFI is used for the visualisation of the locally resolved response of the bulk magnetic domain structures under the influence of externally applied magnetic fields. In the first part, the domain formation and growth along the initial magnetisation curve (0-6000 A/m) up to saturation in static DC magnetic fields was studied. For decreasing field values, the visualisation of the recurrence of the hysteretic domain structure down to the remanent (0 A/m) state is given. A correlation of the grain orientation and the corresponding basic and supplementary domain structure is given. In the second part, the DFI is used to investigate the response of magnetic domain walls to dynamic AC magnetic excitations. The visualisation of the domain wall motion under influence of alternating magnetic fields is performed. In detail, scans combining varying levels of an offset DC (0-30 A/m), oscillation amplitude A (0-1500 A/m), and oscillation frequency f (0-200 Hz) are conducted. By increasing the amplitude while maintaining constant values of DC and f, the transition from a frozen domain wall structure to a mobile one is recorded. Vice versa, increasing f while keeping A and DC constant led to the reverse transition from a mobile domain wall structure into a frozen one. It is shown that varying both, A and f shifts the position of transition region. Higher frequencies require higher oscillation amplitudes to overcome the freezing. The DFI allows for the analysis of the laminations coatings impact to the magnetic structures. To visualise the stress effect of the coating to the underlying domain formation an uncoated lamination is investigated with stepwise increasing applied external tensile stresses up to 20MPa. The domain configurations of the intermediate stress states are imaged and the original domain structure of the coated state is reproduced. To verify the results, complementary experiments using Kerr microscopy, Faraday imaging, small-angle neutron scattering and Laue X-ray diffraction were performed. The here presented findings allow for new insights into macromagnetism and enable new approaches in the field of descriptive models for bulk macromagnetism. Furthermore the results have the potential to further improve the properties of GO-steels used in industrial transformer applications.

EPFL2016

The role of mechanical hysteresis source in mechanical and mechanobiological performances of load-bearing biomaterials

Naser Nasrollahzadeh Mamaghani

Tissue engineering is a promising approach for articular cartilage regeneration as no satisfactory treatment is actually available for cartilage, partly due to the very limited self-healing capability of this tissue. To successfully induce a cartilaginous tissue formation, however, a variety of contributing factors either from a biological or engineering standpoint should be optimized. In particular, sufficient biophysical signals should be provided to promote the response of the spatially distributed cells in a biomimetic three dimensional (3D) scaffold. Given the significance of cartilage dissipative properties when it is submitted to loading, we hypothesized that hydrogels presenting adequate viscoelastic properties could provide a mechano-mimetic niche that would support chondrocyte precursors proliferation and differentiation. In addition, a preserved hysteresis source is an essential feature for a tough biomaterial with robust mechanical behavior. As a consequence, a carefully designed dissipative hydrogels might simultaneously enhance its mechanical and mechanobiological performances. Therefore, the development of mechanically and biologically functional hydrogels as model systems to study the mechanobiology of cartilage is the central aim of this thesis. Indeed, elucidating the aspects of cartilage mechanobiology can facilitate the clinical translation of engineered construct as the mechanical cues significantly influence the cells response. In parallel, temperature evolution due to the conversion of the dissipated energy to heat following cyclic loading brings new insights to interpret the effects of mechanical forces on the cells behavior. In this context, identifying the optimal thermo-mechanical stimulation of cells-laden hydrogel can positively contribute to the development of engineered cartilage. Given hydrogel as a biphasic material, it can dissipate the input mechanical energy via interstitial fluid frictional drag and macromolecular network resistance to deformation. These two fundamentally different physical mechanisms, which induce a mechanical hysteresis, can be controlled by the biphasic materialâs permeability and by the composition of its network, respectively. Accordingly, we firstly developed an experimental method to directly measure the strain-dependent permeability of visco-porous hydrogels. Based on the correlation between the permeability-composition pair and the hydrogel dissipation, an original combination of flow-dependent and flow-independent dissipation source was proposed for the design of biomechanically functional hydrogels. In particular, a heteroporous yet low permeable, fatigue resistance hydrogel was developed via an hybrid crosslinking strategy presenting weak physical bonds and strong covalent bonds. We showed that hydrogels with the same level of stiffness and energy dissipation respond to fatigue loading in a significant different way, depending on their preserved or shrank hysteresis curves during cyclic loading. By developing a semi-inverse poro-viscoelastic model, we also showed that the load is partly carried by the solid phase in hybridly crosslinked hydrogel with low permeability thanks to the support of the pressurized fluid. Before evaluating the role of the dissipation mechanisms in chondrogenesis, we developed a reproducible cell seeding technique via a combination of computational and experimental approaches. In particular, the optimized compression release-induced suction

EPFL2019

Optimisation of low pressure processing for honeycomb sandwich structures

Sandra Sequeira Lopes Tavares

Vacuum-bag processing of honeycomb sandwich structures faces particular challenges compared to autoclave sandwich fabrication for aeronautics, a consequence of using, at the most, atmospheric pressure for their manufacturing. In particular, the adhesion of the skin to the honeycomb core is reduced and the skins tend to have higher values of porosity. On the other hand, autoclave processing is expensive, in particular for large structures, and a growing interest has been observed for vacuum-bag only processing of sandwich structures. During honeycomb sandwich cure, the skin represents a barrier to air flow between the honeycomb and the vacuum-bag so the air transport through the prepreg, adhesive and consumables or other additional materials may be a crucial factor to increase skin debulking, reduce void content and extract air from the honeycomb cells. The pressure inside the honeycomb is, therefore, a result of the through thickness permeability to air of the skins and vacuum pump work. The goal of this thesis is to develop methods for improving the low pressure processing of honeycomb sandwich structures by quantifying the through thickness air permeability of fibre reinforced composites during cure and analysing related processing issues and governing phenomena. An experimental method based on a falling pressure measurement was proposed to evaluate the through thickness air permeability of prepregs during cure, with two set-up variants. One concerns the measurement of the inherent air permeability and the other applies to processing conditions, implying the use of both consumables and vacuum-bag. The methods were successfully tested and fulfil the criterions used in soil science for the evaluation of the air permeability. Prepreg and adhesive permeabilities were determined separately and in skin combination. Prepreg permeability to air during cure varies between 10-19 m2 and 10-17 m2 and was found to depend on the evolution of the resin viscosity, which shifts from an initially immobile phase to a mobile one and then back to an immobile phase. The adhesive film was found to have very low initial permeability, at least two orders of magnitude lower than that of the prepreg. A range of initial skin through thickness air permeability could be achieved by perforating the prepreg plies, the adhesive layer, or a combination of both. An adhesive deposition method which results in the centre of honeycomb cells being free of adhesive was also tested. A corresponding range of achievable pressure was measured inside the honeycomb. The evolution of the through thickness permeability with the curing cycle was determined for each case. The adhesive layer was identified as the element that reduces the initial through thickness air permeability the most in skin manufacturing. This suggests that one of the ways of increasing the initial through thickness air permeability of the skin is to modify the permeability of the adhesive layer. The role of the resulting pressure inside the honeycomb on skin-core adhesion and skin quality was then evaluated. Skin permeability was found to control skin-core adhesion through the pressure drop in the honeycomb cells and potential outgassing of the adhesive layer. An optimal range of pressure inside the honeycomb was found to be between 40 kPa and 70 kPa. A process window is proposed for achieving the optimal pressure inside the honeycomb, as a function of the skin permeability and time of vacuum application. A semipreg alternating dry and resin impregnated areas along the fibre bed surface was also investigated as an alternative to prepreg in skin manufacturing. The semipreg through thickness air permeability before cure is approximately three orders of magnitude higher than that of a unidirectional prepreg impregnated with the same resin, thus allowing the reduction of air pressure in the honeycomb. A model was proposed for the air permeability change during cure, as dry areas get infiltrated. Due to resin pouring inside the honeycomb cells, this type of semipreg is viable as a skin only if combined with a material that has low permeability to resin, e.g., a prepreg. The resulting initial pressure in the honeycomb cells might then be tailored to specific needs. Finally, it was possible to produce sandwich samples combining a consolidation system, such as a prepreg, with an infiltration system, as wet lay-up or with a semipreg. The combination of a prepreg with a semipreg revealed to be a very practical and clean system, where it is possible to have the same resin in both materials. Moreover, it allows to tailor the initial honeycomb pressure as well as during cure, and to have the initial permeability assessed.

EPFL2009