Nonlinear response of glassâ€“forming dispersions under applied timeâ€“dependent deformations

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In this thesis, I have discussed the nonlinear response of glassâ€“forming dispersions under applied timeâ€“dependent deformations. This topic provides insight in the dynamics of such materials close to the glass transition. The nonlinear response offers a further comprehension of the glass transition and the nature of the glass. I have described the process of yielding as a transition from the anelastic stress response to plastic flow and as a transition from a deformed to a shearâ€“melted glass. The schematic MCT model, which I have used to describe the response to timeâ€“dependent shear flow and to applied stress, gives the transient timeâ€“dependence of the response. By omitting the waveâ€“vector dependence, I have lost structural information. I can interpret the structural dynamics only in the context of the microscopic MCT theory, by relating the density correlation function of the schematic model to the corresponding correlation functions of the microscopic theory.

By an instantaneous change of direction of the imposed shear flow, I have studied the historyâ€“dependent response of materials in proximity of the glass transition. In equilibrium physics, a change in the observables can be explained by a change of the variables defining each state. The schematic MCT model obtains a nonequilibrium observable by taking the whole deformation history into account, based on the ITTâ€“MCT approach [10].

Using this historyâ€“dependence of the response to a shear reversal, I have probed the dynamics at the time of the reversal. I have rationalized the phenomena of residual strains, decreased overshoots and a softer apparent elasticity as results of stress contributions of the preshear, the shear flow before the reversal of its direction. By systematic computations of the quantifying observables of these phenomena for preshear strains from zero to one, I have discussed the effect of the yielding transition on the preshear dependence. This discussion is consistent, with the interpretation of the yielding as the transition from a (mostly) reversible anelastic regime to the steady state of irreversible flow.

The densityâ€“dependence of the elasticity of the quiescent glass and the shearâ€“rate dependence of transient stress overshoots and steady states persists in the results for a shearâ€“flow reversal. I have traced the scaling with the separation parameter, that corresponds to a relative density, back to the scaling of the nonergodicity parameter.

Using the numerical inversion of the schematic MCT model, I have computed the strain response under applied constant stress, known as creep. The inversion simplifies the analysis of the relation between strainâ€“controlled and stressâ€“controlled rheology. In the linear response regime, for both stress steps and stress ramps, I have connected every increase of the strain

to a known dissipative process in the glass. The onset of the nonlinear response depends in my computations on the same mechanisms related to the yielding of a glass under steady shear.

I can rule out for the schematic MCT model, that asymptotic flow is caused by an applied stress smaller than the dynamical yield stress. Any applied stress larger than the yield stress results in asymptotic flow. I have introduced a schematic overview, which separates glassy from fluid dynamics and linear from nonlinear response. The yielding transition is connected to the transition from linear to nonlinear response of the glass.

The results for the stress response after a shearâ€“flow reversal and for strain response under applied stress show new aspects on the onset of nonlinear response. Stress and stain response can be described by the same fundamental principles. In this work, the process of homogeneous yielding is attributed to a collective cage breaking of neighboring particles, represented in ITTâ€“MCT by a dephasing of the derivatives of the static structure factor [41].

To advance the discussion of the transient time dependence of yielding, the underlying structural mechanisms should be studied in the microscopic MCT and in Brownian dynamics simulations.

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## ISO 690

FRAHSA, Fabian, 2015.*Nonlinear response of glassâ€“forming dispersions under applied timeâ€“dependent deformations*[Dissertation]. Konstanz: University of Konstanz

## BibTex

@phdthesis{Frahsa2015Nonli-30953, year={2015}, title={Nonlinear response of glassâ€“forming dispersions under applied timeâ€“dependent deformations}, author={Frahsa, Fabian}, address={Konstanz}, school={UniversitĂ¤t Konstanz} }

## RDF

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The nonlinear response offers a further comprehension of the glass transition and the nature of the glass. I have described the process of yielding as a transition from the anelastic stress response to plastic flow and as a transition from a deformed to a shearâ€“melted glass. The schematic MCT model, which I have used to describe the response to timeâ€“dependent shear flow and to applied stress, gives the transient timeâ€“dependence of the response. By omitting the waveâ€“vector dependence, I have lost structural information. I can interpret the structural dynamics only in the context of the microscopic MCT theory, by relating the density correlation function of the schematic model to the corresponding correlation functions of the microscopic theory.<br />By an instantaneous change of direction of the imposed shear flow, I have studied the historyâ€“dependent response of materials in proximity of the glass transition. In equilibrium physics, a change in the observables can be explained by a change of the variables defining each state. The schematic MCT model obtains a nonequilibrium observable by taking the whole deformation history into account, based on the ITTâ€“MCT approach [10].<br />Using this historyâ€“dependence of the response to a shear reversal, I have probed the dynamics at the time of the reversal. I have rationalized the phenomena of residual strains, decreased overshoots and a softer apparent elasticity as results of stress contributions of the preshear, the shear flow before the reversal of its direction. By systematic computations of the quantifying observables of these phenomena for preshear strains from zero to one, I have discussed the effect of the yielding transition on the preshear dependence. This discussion is consistent, with the interpretation of the yielding as the transition from a (mostly) reversible anelastic regime to the steady state of irreversible flow.<br />The densityâ€“dependence of the elasticity of the quiescent glass and the shearâ€“rate dependence of transient stress overshoots and steady states persists in the results for a shearâ€“flow reversal. I have traced the scaling with the separation parameter, that corresponds to a relative density, back to the scaling of the nonergodicity parameter.<br />Using the numerical inversion of the schematic MCT model, I have computed the strain response under applied constant stress, known as creep. The inversion simplifies the analysis of the relation between strainâ€“controlled and stressâ€“controlled rheology. In the linear response regime, for both stress steps and stress ramps, I have connected every increase of the strain<br />to a known dissipative process in the glass. The onset of the nonlinear response depends in my computations on the same mechanisms related to the yielding of a glass under steady shear.<br />I can rule out for the schematic MCT model, that asymptotic flow is caused by an applied stress smaller than the dynamical yield stress. Any applied stress larger than the yield stress results in asymptotic flow. I have introduced a schematic overview, which separates glassy from fluid dynamics and linear from nonlinear response. The yielding transition is connected to the transition from linear to nonlinear response of the glass.<br />The results for the stress response after a shearâ€“flow reversal and for strain response under applied stress show new aspects on the onset of nonlinear response. Stress and stain response can be described by the same fundamental principles. In this work, the process of homogeneous yielding is attributed to a collective cage breaking of neighboring particles, represented in ITTâ€“MCT by a dephasing of the derivatives of the static structure factor [41].<br />To advance the discussion of the transient time dependence of yielding, the underlying structural mechanisms should be studied in the microscopic MCT and in Brownian dynamics simulations.</dcterms:abstract> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/30953/3/Frahsa_0-289487.pdf"/> <dc:language>eng</dc:language> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-05-15T08:35:54Z</dcterms:available> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/30953/3/Frahsa_0-289487.pdf"/> <dc:contributor>Frahsa, Fabian</dc:contributor> <dc:creator>Frahsa, Fabian</dc:creator> <dcterms:title>Nonlinear response of glassâ€“forming dispersions under applied timeâ€“dependent deformations</dcterms:title> <foaf:homepage rdf:resource="http://localhost:8080/"/> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-05-15T08:35:54Z</dc:date> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> </rdf:Description> </rdf:RDF>