The stress driven growth of an expanding precipitate at a crack tip is studied. The material is assumed to be linearly elastic, and the expansion is considered to be isotropic or transversely isotropic. The extent of the precipitate is expected to be small as compared with the crack length and distance to boundaries. The problem has only a single length scale given by the squared ratio of the stress intensity factor and a critical hydrostatic stress that initiates the growth of the precipitate. Therefore, the growth occurs under self-similar conditions. The equations on non-dimensional form show that the free parameters are expansion strain, degree of anisotropy and Poisson's ratio. It is found that the precipitate, once initiated, grows without remote load for expansion strains above a critical value. The anisotropy of the expansion strongly affects the shape of the precipitate but does not have a large effect on the crack tip shielding.

A model is established that describes stress driven diffusion, resulting in formation and growth of an expanded precipitate at the tip of a crack. The new phase is transversely isotropic. A finite element method is used and the results are compared with a simplified analytical theory. A stress criterium for formation of the precipitate is derived by direct integration of the Einstein-Smoluchowski law for stress driven diffusion. Thus, the conventional critical concentration criterium for precipitate growth can be replaced with a critical hydrostatic stress. The problem has only one length scale and as a consequence the precipitate grows under self-similar conditions. The length scale is given by the stress intensity factor, the diffusion coefficient and critical stress versus remote ambient concentrations. The free parameters involved are the expansion strain, the degree of anisotropy and Poisson's ratio. Solutions are obtained for a variation of the first two. The key result is that there is a critical phase expansion strain below which the growth of the new phase is stable and controlled by the stress intensity factor. For supercritical expansion strains, the precipitate grows even without remote load. The anisotropy of the expansion strongly affects the shape of the precipitate, but does not have a large effect on the crack tip shielding. (C) 2018 The Authors. Published by Elsevier B.V.

The stress fields of expanding (precipitation) and contracting (dissolution) hydride plates were computed by finite element method using Zr–H solid solution and hydride properties at 25, 200 and 400 °C for fully and semi-constrained hydride plates. For the first time simultaneous hydride expansion and matrix contraction and vice-versa have been considered in a simulation of hydride precipitation and dissolution, respectively. It was observed that a fully constrained expanding hydride plate exerts a tensile stress field in the matrix close to the edge of the hydride plate while a partially contracting hydride plate exerts a tensile stress field in the hydride plate as well as a large compressive stress in the surrounding matrix close to the edge of the hydride plate. It is suggested that a compressive stress component in the matrix acting normal to a partially shrinking hydride plate could possibly explain an enhanced resistance to hydride embrittlement of Zr-alloy at elevated temperature.

Bone modeling and remodeling has been the subject of extensive experimental studies. There have been several mathematical models proposed to explain the observed behavior, as well. A different approach is taken here in which the bone is treated from a macroscopic view point. In this investigation, a one-dimensional analytical model is used to shed light on the factors which play the greatest role in modeling or growth of cortical bone at the periosteal surface. It is presumed that bone growth is promoted when increased amounts of bone nutrients, such as nitric oxide synthase (NOS) or messenger molecules, such as prostaglandin E2 (PGE2), seep out to the periosteal surface of cortical bone and are absorbed by osteoblasts. The transport of the bone nutrients is assumed to be a strain controlled process. Equations for the flux of these nutrients are written for a one-dimensional model of a long bone. The obtained partial differential equation is linearized and solved analytically. Based upon the seepage of nutrients out of the bone, the effect of loading frequency, number of cycles and strain level is examined for several experiments that were found in the literature. It is seen that bone nutrient seepage is greatest on the tensile side of the bone; this location coincides with the greatest amount of bone modeling

To honour the memory of Knut Bertram Broberg, and to promote continuing work on the many ideas which he shared so generously with students and colleagues throughout his lifetime, a symposium was arranged at University College of Dublin in 2007. The idea was to create an informal atmosphere, and to keep the num- ber of participants fairly low. This has now become a bi-annual symposium with the highlight being one or two lectures by outstanding world-class scientists. The second Broberg Memorial Symposium was arranged by the Lund Institute of Technology in Sweden (LTH) in May 2009. The venue of the conference was a renais- sance castle, Trolleholm, that was put to our disposal by the courtesy of the Rector of LTH. Trolleholm was once the home of Sophia Brahe whose careful obser- vations of planetary orbits later was used by Johannes Kepler to develop his laws of planetary motion. Kepler was at the time working as an assistant to Sophia’s brother Tycho Brahe.

Thin hard coatings on components and tools are used increasingly due to the rapid development in deposition techniques, tribological performance and application skills. The residual stresses in a coated surface are crucial for its tribological performance. Compressive residual stresses in PVD deposited TiN and DLC coatings were measured to be in the range of 0.03–4 GPa on steel substrate and 0.1–1.3 GPa on silicon. MoS2 coatings had tensional stresses in the range of 0.8–1.3 on steel and 0.16 GPa compressive stresses on silicon. The fracture pattern of coatings deposited on steel substrate were analysed both in bend testing and scratch testing. A micro-scale finite element method (FEM) modelling and stress simulation of a 2 μm TiN-coated steel surface was carried out and showed a reduction of the generated tensile buckling stresses in front of the sliding tip when compressive residual stresses of 1 GPa were included in the model. However, this reduction is not similarly observed in the scratch groove behind the tip, possibly due to sliding contact-induced stress relaxation. Scratch and bending tests allowed calculation of the fracture toughness of the three coated surfaces, based on both empirical crack pattern observations and FEM stress calculation, which resulted in highest values for TiN coating followed by MoS2 and DLC coatings, being KC = 4–11, about 2, and 1–2 MPa m1/2, respectively. Higher compressive residual stresses in the coating and higher elastic modulus of the coating correlated to increased fracture toughness of the coated surface.

Delayed hydride cracking (DHC) velocity was determined at 203, 227, 250 and 283 °C using 17 mm width curved compact toughness specimens machined from an unirradiated Zr–2.5 wt.% Nb pressure tube spool, gaseously charged with 60 ppm of hydrogen by weight. Single CT specimen was used to determine DHC velocity at a constant temperature for a range of stress intensity factor (KI) obtained by load drop method. For a given temperature and KI > 15 MPa m1/2, DHC velocity was found to be practically independent of KI. For 15 > KI > 10 MPa m1/2, DHC velocity decreased significantly with decrease in stress intensity factor and extrapolation of the data suggested the threshold stress intensity factor to be about 9–11 MPa m1/2 in the aforementioned temperature range. The activation energy associated with DHC was observed to be 35.1 kJ/mol.