RESUMEN

A system of edge cracks was applied to polished (010) surfaces of K-rich gem-quality alkali feldspar by diffusion-mediated cation exchange between oriented feldspar plates and a Na-rich NaCl-KCl salt melt. The cation exchange produced a Na-rich layer at and beneath the specimen surface, and the associated strongly anisotropic lattice contraction lead to a tensile stress state at the specimen surface, which induced fracturing. Cation exchange along the newly formed crack flanks produced Na-enriched diffusion halos around the cracks, and the associated lattice contraction and tensile stress state caused continuous crack growth. The cracks nucleated with non-uniform spacing on the sample surface and quickly attained nearly uniform spacing below the surface by systematic turning along their early propagation paths. In places, conspicuous wavy cracks oscillating several times before attaining their final position between the neighboring cracks were produced. It is shown that the evolution of irregularly spaced towards regularly spaced cracks including the systematic turning and wavyness along the early propagation paths maximizes the rate of free energy dissipation in every evolutionary stage of the system. Maximization of the dissipation rate is suggested as a criterion for selection of the most probable evolution path for a system undergoing chemically induced diffusion mediated fracturing in an anisotropic homogeneous brittle material. Supplementary Information: The online version contains supplementary material available at 10.1007/s00269-022-01183-9.

RESUMEN

Thin metal films deposited on polymer substrates are used in flexible electronic devices such as flexible displays or printed memories. They are often fabricated as complicated multilayer structures. Understanding the mechanical behavior of the interface between the metal film and the substrate as well as the process of crack formation under global tension is important for producing reliable devices. In the present work, the deformation behavior of copper films (50-200 nm thick), bonded to polyimide directly or via a 10 nm chromium interlayer, is investigated by experimental analysis and computational simulations. The influence of the various copper film thicknesses and the usage of a brittle interlayer on the crack density as well as on the stress magnitude in the copper after saturation of the cracking process are studied with in situ tensile tests in a synchrotron and under an atomic force microscope. From the computational point of view, the evolution of the crack pattern is modeled as a stochastic process via finite element based cohesive zone simulations. Both, experiments and simulations show that the chromium interlayer dominates the deformation behavior. The interlayer forms cracks that induce a stress concentration in the overlying copper film. This behavior is more pronounced in the 50 nm than in the 200 nm copper films.

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Arachnid slit sensilla respond to minute strains in the exoskeleton. After having applied finite element (FE) analysis to simplified arrays of five straight slits (Hössl et al. J Comp Physiol A 193:445-459, 2007) we now present a computational study of the effects of more subtle natural variations in geometry, number and arrangement of slits on the slit face deformations. Our simulations show that even minor variations in these parameters can substantially influence a slit's directional response. Using white-light interferometric measurements of the surface deformations of a lyriform organ, it is shown that planar FE models are capable of predicting the principal characteristics of the mechanical responses. The magnitudes of the measured and calculated slit face deformations are in good agreement. At threshold, they measure between 1.7 and 43 nm. In a lyriform organ and a closely positioned loose group of slits, the detectable range of loads increases to approximately 3.5 times the range of the lyriform organ alone. Stress concentration factors (up to ca. 29) found in the vicinity of the slits were evaluated from the models. They are mitigated due to local thickening of the exocuticle and the arrangement of the chitinous microfibers that prevents the formation of cracks under physiological loading conditions.

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RESUMEN

Arachnid strain sensitive slit sensilla are elongated openings in the cuticle with aspect ratios (slit length l/slit width b) of up to 100. Planar Finite Element (FE) models are used to calculate the relative slit face displacements, Dc, at the centers of single slits and of arrangements of mechanically interacting slits under uni-axial compressive far-field loads. Our main objective is to quantitatively study the role of the following geometrical parameters in stimulus transformation: aspect ratio, slit shape, geometry of the slits' centerlines, load direction, lateral distance S, longitudinal shift lambda, and difference in slit length Deltal between neighboring slits. Slit face displacements are primarily sensitive to slit length and load direction but little affected by aspect ratios between 20 and 100. In stacks of five parallel slits at lateral distances typical of lyriform organs (S=0.03 l) the longitudinal shift lambda substantially influences slit compression. A change of lambda from 0 to 0.85 l causes changes of up to 420% in Dc. Even minor morphological variations in the arrangements can substantially influence the stimulus transformation. The site of transduction in real slit sensilla does not always coincide with the position of maximum slit compression predicted by simplified models.

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RESUMEN

Stimulus transformation in arthropod mechanoreceptive hairs is dominated by the mechanical properties of both the hair shaft and the hair's articulation. Here a mathematical model of the hair's articulation is developed based on simple relationships relevant for every anisotropic articulation. The mechanical behavior regarding deflection under load of a variety of hairs can be described quantitatively by using only two (in the case of double symmetric characteristics) or four parameters (in the case of only one symmetry): (1) joint stiffness S p in the preferred direction of deflection, (2) joint stiffness St in a plane transversal to the preferred direction, and (3, 4) the values of stiffness S for opposite directions of deflection. The applicability of the model was tested by measuring these stiffnesses S of spider tactile hair joints by deflecting the hairs statically in different directions. For comparison, data in the literature on insect and spider hairs sensitive to air flow were analyzed. The equation presented describes the directional characteristics of a wide range of structurally different cuticular hairs. It can also be used as a mathematical description of the joint mechanics when modeling the mechanics of hairs, for instance, by applying methods such as Finite Element Analysis.

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