Mechanical properties of spruce wood cell walls by nanoindentation

In order to study the effects of structural variability, nanoindentation experiments were performed in Norway spruce cell walls with highly variable cellulose microfibril angle and lignin content. Contrary to hardness, which showed no statistically significant relationship with changing microfibril angle and lignin content, the elastic modulus of the secondary cell wall decreased significantly with increasing microfibril angle. While the elastic moduli of cell walls with large microfibril angle agreed well with published values, the elastic moduli of cell walls with small microfibril angle were clearly underestimated in nanoindentation measurements. Hardness measurements in the cell corner middle lamella allowed us to estimate the yield stress of the cell-wall matrix to be 0.34±0.16 GPa. Since the hardness of the secondary cell wall was statistically not different from the hardness of the cell corner middle lamella, irrespective of high variability in cellulose microfibril angle, it is proposed that compressive yielding of wood-cell walls is a matrix-dominated process. PACS 83.80.Mc     

Strain-induced morphologies during homogeneous phase separation in alloys

When precipitates grow with a lattice misfit inside a matrix having cubic crystal symmetry, a transition may occur from an isotropic arrangement of the precipitates to an alignment along the cubic directions of the crystal. Furthermore, if a uniaxial external strain is applied, an additional transition towards tetragonal symmetry can occur by fusion of the precipitates into large plates perpendicular (or long rods parallel) to the direction of applied strain (“rafting”). Recent experiments on Ni-Al-Mo alloys as well as computer simulations relating to these two transitions are reviewed.     

Modeling of Phase Separation in Alloys with Coherent Elastic Misfit

Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) behavior of alloys. If the elastic moduli are different in the two phases, the elastic interactions may accelerate, slow down or even stop the phase separation process. If the material is elastically anisotropic, the precipitates can be shaped like plates or needles instead of spheres and can arrange themselves into highly correlated patterns. Tensions or compressions applied externally to the specimen may have a strong effect on the shapes and arrangement of the precipitates. In this paper, we review the main theoretical approaches that have been used to model these effects and we relate them to experimental observations. The theoretical approaches considered are (i) macroscopic models treating the two phases as elastic media separated by a sharp interface, (ii) mesoscopic models in which the concentration varies continuously across the interface, and (iii) microscopic models which use the positions of individual atoms.     

Statistical model of the habit and arrangement of mineral crystals in the collagen of bone

Randomly colored space tesselations are considered as models for the mineral/organic structure of bone. First, it is shown that the structure function for such models is always proportional to the average form factor of the individual tiles and hence independent of the mineral density in the sample. Then the structure function is calculated for three such models: for model I, based on a hexagonal, and model 2, on a Poisson-Voronoi tesselation of the plane and for model 3, based on a random tesselation of the line. These results are compared to experimental structure functions measured by small-angle scattering and excellent agreement is obtained between model 2 and the bone from mice and rats, as well as between model 3 and calcified turkey leg tendon. Divergent conclusions following recent experiments by small-angle x-ray scattering and by electron microscopy are discussed in the light of these structural models and an explanation is proposed which might remove the discrepancy.Dedicated to Prof. Oliver Penrose on the occasion of his 65th birthday.     

Surface-directed spinodal decomposition on a macroscopic scale in a nitrogen and carbon alloyed steel

Interactions with the macroscopic specimen surface can profoundly modify phase-separation processes. This has previously been observed in liquids and polymer films and is theoretically described by the theory of surface-directed spinodal decomposition (SDSD). Here we report first observations of SDSD in a metallic alloy on a macroscopic scale. The influence of the surface leads to the development of concentric domains extending over the whole 10 mm thick cylindrical steel specimen, due to long-range interactions via elastic stresses and long-range diffusion of the interstitial elements nitrogen and carbon.     

Energy dissipation and stability of propagating surfaces

Thermodynamic equilibrium states are given by the minimum of a convex free energy function with suitable boundary conditions. Nonconvexity may lead to the coexistence of several phases and the classical Gibbs phase rule allows constructing their equilibrium properties (e.g., density or pressure). Within the framework of nonequilibrium thermodynamics, the maximization of energy dissipation (under suitable boundary conditions) can be used as an extremal principle to find stationary states. We show that stationary states generally exist for convex energy dissipation functions and that nonconvexity leads to metastable and unstable states. A geometric argument, similar in spirit to Gibbs' double-tangent construction, yields the stability limits of stationary states. This argument is applied to study a classical problem of materials science, namely the motion of a grain boundary under the influence of solute drag.