3D characterisation of hydrogen environmentally assisted cracking during static loading of AA7449-T7651

In this investigation, synchrotron X-ray microtomography was used to perform 3D in situ observations of crack initiation and growth during hydrogen environmentally assisted cracking (HEAC) in tensile samples of AA7449-T7651. Two smooth tensile samples with a 1 mm diameter gauge section were held at a fixed displacement ($$\approx 30$$ ≈ 30 % of yield stress) in warm, moist air ($$\approx 76\,^\circ $$ ≈ 76 ∘ C, 73% relative humidity). The samples were then imaged repeatedly using X-ray tomography until they fractured completely. The tomograms showing the nucleation and evolution of intergranular cracks were correlated with electron microscopy fractographs. This enabled the identification of crack initiation sites and the characterisation of the crack growth behaviour relative to the microstructure. The samples were found to fracture within an environmental exposure time of 240 min. Some cracks in both samples nucleated within an exposure time of 80 min (33–40% of the total lifetime). Many cracks were found to nucleate both internally and at the sample surface. However, only superficial cracks contributed to the final fracture surface as they grew faster owing to the direct environmental exposure and the larger crack opening. HEAC occurred prominently via brittle intergranular cracking, and cracks were found to slow down when approaching grain boundary triple junctions. Additionally, crack shielding from nearby cracks and the presence of coarse Al–Cu–Fe particles at the grain boundaries were also found to temporarily reduce the crack growth rates. After prolonged crack growth, the HEAC cracks displayed ductile striations and transgranular fracture, revealing a change in the crack growth mechanism at higher stress intensity factors.

Unitary Boundary Pairs for Isometric Operators in Pontryagin Spaces and Generalized Coresolvents

An isometric operator V in a Pontryagin space $${{{\mathfrak {H}}}}$$ H is called standard, if its domain and the range are nondegenerate subspaces in $${{{\mathfrak {H}}}}$$ H . A description of coresolvents for standard isometric operators is known and basic underlying concepts that appear in the literature are unitary colligations and characteristic functions. In the present paper generalized coresolvents of non-standard Pontryagin space isometric operators are described. The methods used in this paper rely on a new general notion of boundary pairs introduced for isometric operators in a Pontryagin space setting. Even in the Hilbert space case this notion generalizes the earlier concept of boundary triples for isometric operators and offers an alternative approach to study operator valued Schur functions without any additional invertibility requirements appearing in the ordinary boundary triple approach.

DIFFUSION NUCLEATION OF CAVITIES IN GRAIN JUNCTIONS OF SUBMICROCRYSTALLINE MATERIALS

The conditions of diffusional cavity nucleation in submicrocrystalline materials processed by the methods of intensive plastic deformation (equal-channel angular pressing, multiaxial forging, high pressure torsion, etc.) are analyzed. To date, the question of the mechanism of nucleation of cavities in such materials remains debatable due to the fact that the processing of materials by the methods of intensive plastic deformation is carried out at high hydrostatic pressures that prevent the appearance of pores. The possibility of diffusive nucleation of nanopores in the region of triple junctions of grains containing negative strain-induced wedge disclinations, generating high tensile stresses in the vicinity of triple junctions, comparable in magnitude to external hydrostatic pressure, is shown. Such junction disclinations inevitably occur at the grain junctions due to the heterogeneity of the plastic deformation through the ensemble of polycrystal grains. It is shown that an important condition for the nucleation of cavities is not only the presence of high internal tensile stresses from junction disclinations, but also an extremely high concentration of nonequilibrium strain-induced vacancies characteristic of submicrocrystalline metals, comparable in values to the vacancy concentration, at temperatures close to solidus. The influence of the strength of junction disclinations, the value of external hydrostatic pressure and the degree of supersaturation of the material by nonequilibriumstrain-induced vacancies on the rate of diffusional nucleation and the volume of critical pore nuclei is analyzed. It is established that in order to effectively suppress the process of pore formation in the grain boundary triple junctions, it is necessary to apply an external hydrostatic pressure that compensates for internal elastic fields from junction disclinations.

Self-Adjoint Dirac Operators on Domains in $$\mathbb {R}^3$$

In this paper, the spectral and scattering properties of a family of self-adjoint Dirac operators in $$L^2(\Omega ; \mathbb {C}^4)$$ L 2 ( Ω ; C 4 ) , where $$\Omega \subset \mathbb {R}^3$$ Ω ⊂ R 3 is either a bounded or an unbounded domain with a compact $$C^2$$ C 2 -smooth boundary, are studied in a systematic way. These operators can be viewed as the natural relativistic counterpart of Laplacians with boundary conditions as of Robin type. Our approach is based on abstract boundary triple techniques from extension theory of symmetric operators and a thorough study of certain classes of (boundary) integral operators, that appear in a Krein-type resolvent formula. The analysis of the perturbation term in this formula leads to a description of the spectrum and a Birman–Schwinger principle, a qualitative understanding of the scattering properties in the case that $$\Omega $$ Ω is an exterior domain, and corresponding trace formulas.

ANALYSIS USING ELECTROLYTIC LAYER STRIPPING TO DETERMINE THE PARAMETERS OF GRAIN-BOUNDARY DIFFUSION OF COBALT IN POLYCRYSTALLINE NICKEL

A technique for layer-by-layer radiometric analysis using electrolytic layer stripping to determine the parameters of grain-boundary diffusion of cobalt in polycrystalline nickel has been developed. The aim of the work is to develop a complete technological cycle of layer-by-layer radiometric analysis, to select the optimal electrolyte composition for nickel and the conditions for conducting an experiment to remove metal layers with their thickness of 20–200 nm. The studies have been carried out on nickel of nominal purity of 99,98 %. The stabilizing heat treatment of the samples is carried out at a pressure of 10–5 Pa for 2 hours at a temperature of 1273 K. Diffusion annealing is carried out at a pressure of 10–9 Pa in the temperature range of 623–1173 K for 5–30 hours. Concentration profiles have been measured by parallel stripping of layers, which are obtained by electrolytic polishing in a solution based on nickel sulfamate, followed by weighing the sample on a high-precision analytical balance. The difference in weight before and after removal of the layers is used to further calculate the thickness of the removed layers and, as a consequence, the penetration depth of the diffusing. The residual activity of the sample is measured using a digital gamma spectrometer with a NaI (Tl) detector. Before carrying out the experiments, a reference source with a previously known activity has been made to take into account the correction factor due to the radioactive decay of 57Co. The specific layer activity is calculated from the integral remainder of the 122,14 keV line using the Gruzin method. Based on the proposed technique, it is possible to determine the parameters of grain boundary diffusion, such as the diffusion coefficient of grain boundary, triple product and segregation coefficient.