Inferring the flow properties of epithelial tissues from their geometry

Amorphous materials exhibit complex material properties with strongly nonlinear behaviors. Below a yield stress they behave as plastic solids, while they start to yield above a critical stress sigma(c). A key quantity controlling plasticity which is, however, hard to measure is the density P(x) of weak spots, where x is the additional stress required for local plastic failure. In the thermodynamic limit P(x) similar to x(theta) is singular at x = 0 in the solid phase below the yield stress sigma(c). This singularity is related to the presence of system spanning avalanches of plastic events. Here we address the question if the density of weak spots and the flow properties of a material can be determined from the geometry of an amorphous structure alone. We show that a vertex model for cell packings in tissues exhibits the phenomenology of plastic amorphous systems. As the yield stress is approached from above, the strain rate vanishes and the avalanches size S and their duration tau diverge. We then show that in general, in materials where the energy functional depends on topology, the value x is proportional to the length L of a bond that vanishes in a plastic event. For this class of models P(x) is therefore readily measurable from geometry alone. Applying this approach to a quantification of the cell packing geometry in the developing wing epithelium of the fruit fly, we find that in this tissue P(L) exhibits a power law with exponents similar to those found numerically for a vertex model in its solid phase. This suggests that this tissue exhibits plasticity and non-linear material properties that emerge from collective cell behaviors and that these material properties govern developmental processes. Our approach based on the relation between topology and energetics suggests a new route to outstanding questions associated with the yielding transition.

Arrested demixing opens route to bigels

Maxim Belushkin, Nicolas Dorsaz, Giuseppe Foffi, Francesco Varrato

Understanding and, ultimately, controlling the properties of amorphous materials is one of the key goals of material science. Among the different amorphous structures, a very important role is played by colloidal gels. It has been only recently understood that colloidal gels are the result of the interplay between phase separation and arrest. When short-ranged attractive colloids are quenched into the phase-separating region, density fluctuations are arrested and this results in ramified amorphous space-spanning structures that are capable of sustaining mechanical stress. We present a mechanism of aggregation through arrested demixing in binary colloidal mixtures, which leads to the formation of a yet unexplored class of materials-bigels. This material is obtained by tuning interspecies interactions. Using a computer model, we investigate the phase behavior and the structural properties of these bigels. We show the topological similarities and the geometrical differences between these binary, interpenetrating, arrested structures and their well-known monodisperse counterparts, colloidal gels. Our findings are supported by confocal microscopy experiments performed on mixtures of DNA-coated colloids. The mechanism of bigel formation is a generalization of arrested phase separation and is therefore universal.

Natl Acad Sciences2012

Constitutive behavior and fracture properties of tempered martensitic steels for nuclear applications

Raul Alejandro Bonadé

In this study, the tensile and fracture properties and the microstructure of the reduced-activation tempered martensitic steel Eurofer97 have been investigated. This technical alloy is a 9%Cr steel developed within the European fusion material research program. To a lesser extend, the plastic flow properties of a equiaxed ferritic Fe9%Cr model alloy were also studied for comparison with those of the tempered martensitic structure. The main objectives of this work are described hereafter: to correlate the microstructural features with the plastic flow properties measured by the tensile tests for both the Eurofer97 steel and the model alloy. The correlation established should be reflected in a physically-based model of plastic flow. to study the fracture properties of the Eurofer97 steel in details in the lower ductile-to-brittle transition region. to calculate with finite element modeling the stress fields at the crack tip. This information is further used in conjunction with a local approach model for quasi-cleavage to reconstruct the fracture toughness-temperature curve. Tensile tests were carried out at different imposed nominal strain rate at several temperatures from 77K up to 473K, on both the Eurofer97 steel and the Fe9%Cr model alloy. The temperature dependence of the yield stress was precisely determined. As expected for body-centered cubic (BCC) materials, a strong increase of the yield stress by decreasing temperature, below 200 K, was observed. At higher temperatures, the temperature dependence of the yield stress was found much weaker, being associated with the temperature dependence of the shear modulus. Efforts were made to analyze in details the post-yield behavior (strain-hardening) as a function of temperature. The post-yield behavior was modeled using the Kocks phenomenological model based on the competition of storage and annihilation of dislocations. While this model was originally developed for face-centered cubic (FCC) metals where the rate-controlling mechanism of dislocation motion is the dislocation-dislocation interaction, we used is model in the high temperature domain (T>200K) of BCC materials, to model the strain-hardening evolution of the Eurofer97 steel and the model alloy. The values obtained for the key parameters of the model, namely the dislocation mean free path and annihilation coefficient, were found consistent with the microstructural features. The parameters temperature-dependence observed was also consistent with the physics of two basic mechanisms of dislocation storage and annihilation (dynamical recovery). For the low temperature domain, the strain-hardening model was modified to account for the strong Peierls lattice friction, based on an original idea of Rauch. Transmission electron microscopy observations were done to characterize the undeformed microstructures and their evolution with strain. A clear correlation was established between the stress-dependence of the strain-hardening and the microstructures. Fracture toughness tests on the Eurofer97 steel were performed with 0.2T C(T) and 0.4T C(T) specimens in the lower transition. Five temperatures were selected at which many tests were repeated to determine the amplitude of the inherent scatter of quasi-cleavage. The temperature were chosen in such a way that the measure fracture toughness remain below 150 MPa m1/2, which correspond for the 0.4T C(T) at a M value larger than 70 at the highest temperature. Such a M value for 0.4T C(T) specimens is known to ensure enough constraint. An attempt to analyze the experimental data in the framework of the master-curve approach by following the ASTM E-1921 standard was done. It was clearly demonstrated that the assumed shape of the toughness-temperature curve as described in the ASTM E-1921 standard for the reactor pressure vessel steels is not adequate for the tempered martensitic Eurofer97 steel, which present a particularly steep transition. Our Eurofer97 fracture database was then compared to the existing one on another similar steel, the F82H. Differences in the amplitude of the scatter of both steels was found while the lower bound of the toughness-temperature curve, describing the 1% failure probability was shown to be the same. 2D finite element simulations of the compact tension specimens were performed at various temperatures using the constitutive laws determined previously. The stress field around the crack tip were calculated and used to determine a local criterion of quasi-cleavage. The criterion is defined by the attainment of a critical stress encompassing a critical area. The lower bound of the toughness-temperature curve was then successfully reconstructed by using this local criterion. Finally, the relationship between the critical area and the applied stress intensity factor for the C(T) specimen was shown to follow a power law whose coefficients are dependent on the real dimensions of the specimen. Such a relationship allows scaling the C(T) toughness data from one size to another in case of in-plane constraint loss.

EPFL2006

Electrophoretic deposition of multi-scale structured TiO2 surfaces

The long term fixation of biomedical implants constitutes an issue in the clinical praxis. Implant fixation can be improved by functionalizing its surface. In fact, the tissue response around an implant is conditioned by its surface morphological and chemical properties. Coatings for implants (orthopedic and dental) function at the bone-implant fixation interface. As proved by research activities in the biomedical field, coatings with topographic features in the nano- and micro-range are promising in terms of enhanced osteointegration, thus improved implant fixation. As for surface chemistry, titanium dioxide (TiO2) is an estabilished material for biomedical implants thanks to its outstanding physical and chemical properties such as high corrosion resistance and good biocompatibility. Electrophoretic deposition (EPD) is a simple and versatile coating technique. According to literature, EPD is an emerging potential coating technique for biomedical implants. In this work, the use of EPD in the preparation of TiO2 coatings characterized by a controlled multi-scale structured surface was addressed. For this aim, EPD was combined with a new procedure of particle functionalization and with the use of a fugitive spacer (polystyrene, PS) for the sintering treatment. A control and better understanding of the EPD process were achieved through a preliminary parametric study on EPD of TiO2 nanoparticles and PS microbeads. Particle concentration was found to play a key role in the EPD deposit formation of TiO2 nanoparticles (cathodic) and PS microbeads (anodic). A threshold value of particle concentration was identified, below which no deposit growth occurred. An interpretation of this finding was provided on the base of a new formulation of the EPD deposition mechanism. The results of the particle concentration study contributed to the preparation of suspensions with TiO2-PS composite particles, which could be used for cathodic EPD. Composite TiO2-PS particles with TiO2 nanoparticles covering PS microbeads were obtained in a newly developed wet colloidal process based on heterocoagulation and the use of polyelectrolytes. The resulting TiO2-PS particles were cathodically deposited on Ti6Al4V substrates. A sintering post-treatment caused the burning out of the PS beads and the densification of the TiO2 nanoparticles. The desired coatings with controlled micro- and nano-topography were achieved. The investigation on the role of particle concentration in EPD and the new interpretation of the deposition mechanism bring a deeper understanding of the EPD process. The achievement of TiO2 coatings with controlled morphology in the micro- and nano-range prepared by cathodic EPD on Ti6Al4V substrates is a contribution to the ongoing research on biomedical implants. Mechanical tests and surface analysis evaluating wettability and in vitro cell behavior with the achieved coatings are relevant topics for further research.

EPFL2009

Constitutive behavior and fracture properties of tempered martensitic steels for nuclear applications

Raul Alejandro Bonadé

EPFL2006

Electrophoretic deposition of multi-scale structured TiO2 surfaces

EPFL2009