The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Ice formation and accretion may hinder the operation of many systems critical to national infrastructure, including airplanes, power lines, windmills, ships, and telecommunications equipment. Yet despite the pervasiveness of the icing problem, the fundamentals of ice adhesion have received relatively little attention in the scientific literature and it is not widely understood which attributes must be tuned to systematically design “icephobic” surfaces that are resistant to icing. Here we probe the relationships between advancing/receding water contact angles and the strength of ice adhesion to bare steel and twenty-one different test coatings (∼200−300 nm thick) applied to the nominally smooth steel discs. Contact angles are measured using a commercially available goniometer, whereas the average strengths of ice adhesion are evaluated with a custom-built laboratory-scale adhesion apparatus. The coatings investigated comprise commercially available polymers and fluorinated polyhedral oligomeric silsesquio...

/pdf/relationships-between-water-wettability-and-ice-adhesion-3zdb7rkfa7.pdf

Relationships between Water Wettability and Ice Adhesion

[1] Snow avalanches are a major natural hazard, endangering human life and infrastructure in mountainous areas throughout the world. In many countries with seasonally snow-covered mountains, avalanche-forecasting services reliably warn the public by issuing occurrence probabilities for a certain region. However, at present, a single avalanche event cannot be predicted in time and space. Much about the release process remains unknown, mainly because of the highly variable, layered character of the snowpack, a highly porous material that exists close to its melting point. The complex interaction between terrain, snowpack, and meteorological conditions leading to avalanche release is commonly described as avalanche formation. It is relevant to hazard mapping and essential to short-term forecasting, which involves weighting many contributory factors. Alternatively, the release process can be studied and modeled. This approach relies heavily on snow mechanics and snow properties, including texture. While the effect of meteorological conditions or changes on the deformational behavior of snow is known in qualitative or semiquantitative manner, the knowledge of the quantitative relation between snow texture and mechanical properties is limited, but promising developments are under way. Fracture mechanical models have been applied to explain the fracture propagation, and micromechanical models including the two competing processes (damage and sintering) have been applied to explain snow failure. There are knowledge gaps between the sequence of processes that lead to the release of the snow slab: snow deformation and failure, damage accumulation, fracture initiation, and fracture propagation. Simultaneously, the spatial variability that affects damage, fracture initiation, and fracture propagation has to be considered. This review focuses on dry snow slab avalanches and shows that dealing with a highly porous media close to its melting point and processes covering several orders of scale, from the size of a bond between snow grains to the size of a mountain slope, will continue to be very challenging.

/pdf/snow-avalanche-formation-2blcpjkk9n.pdf

Snow avalanche formation

Three-dimensional Problems of the Theory of Elasticity. By A. I. Lur’e.1964. (Interscience Publishers)

This is the third in a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite-100 such that crack growth in an unbounded plate is simulated. In the first paper crack initiation resulting from stress wave loading to the crack tip as well as crack arrest were reported. It was found that for increasing rates of loading in the microsecond range the stress intensity required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity lower than that which causes initiation under quasi-static loading.

An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching

This paper examines the composite, two-dimensional, linear elastic wedge for singular stresses at its vertex. A full range of wedge boundary and matching conditions is considered. Using separation of variables on the Airy stress function, the usual determinant conditions for singularities of the formO(r
-λ) asr → 0 are established and further conditions are derived for singularities of the formO(r
-λ lnr) asr → 0. The order of the determinant involved in these conditions depends upon the number of materials comprising the wedge. Two systematic methods of expanding the determinant for theN-material wedge are presented.

On the stress singularities in the plane elasticity of the composite wedge

Information on the singular behavior at the vertex of a bi-material wedge is the objective of this paper. A summary of the necessary conditions, which depend heavily on the associated eigenvalue equation, for stress singularities of O(r
-λ 1n r) as r→0 or O(r
-λ) as r→0 is stated. The eigenvalue equations arising from a wide range of boundary and interface conditions are then provided. Bi-material wedge problems that have been subjected to singularity analyses of some generality in the literature are briefly reviewed.

On the singular behavior at the vertex of a bi-material wedge

A set of lab- to structural-scale (0.5 < L < 80 m) in-situ full thickness (1.8 m) fracture tests were conducted on first-year sea ice at Resolute, N.W.T. using self-similar (plan view) edge-cracked square plates. With a size range of 1:160, the data is used, via size effect analyses, to evaluate the influence of scale effects on the fracture behavior of sea ice over the range 10-1 m (laboratory) to 100 m and to predict the scale effect on tensile strength up to ≈ 1000 m. Details of this large-scale sea ice fracture test program are presented in this paper. The experimental results are presented as well as the fracture modeling of the data. The influence of scale on the ice strength and fracture toughness is dramatic. The applicability of various size effect laws are investigated and criteria for LEFM test sizes are presented. For the thick first-year sea ice tested, the size-independent fracture toughness is of order 250 kPa√m, not the 115 kPa√m that is commonly used. The number of grains spanned by the associated test piece is 200, much larger than the number 15 typically quoted for regular tension-compression testing. The size-independent fracture energy is 15 J/m2, while the requisite LEFM test size for the edge-cracked square plate geometry (for loading durations of less than 600 s and an average grain size of 1.5 cm), is 3 m square. Size effect analyses of sub-ranges of the data show that unless the specimen sizes tested are themselves sufficiently large, the true nature of the scale effect is not revealed, which was a concern raised by Leicester 25 years ago. In the case of the fracture tests reported in this paper, based on the lab-scale and field-scale strength data measured between 0.1 and 3 m and using Bažant’s size effect law, it is possible to accurately predict the tensile strengths for all of the remaining tests, up to and including 80 m.

John P. Dempsey

Papers

On the stress singularities in the plane elasticity of the composite wedge

On the singular behavior at the vertex of a bi-material wedge

Scale effects on the in-situ tensile strength and fracture of ice. Part II: First-year sea ice at Resolute, N.W.T.

Stable crack growth in nanostructured Li-batteries

Design criteria for nanostructured Li-ion batteries