John P. Dempsey

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

The wedge subjected to tractions: a paradox resolved

The classical two-dimensional solution provided by Lévy for the stress distribution in an elastic wedge, loaded by a uniform pressure on one face, becomes infinite when the opening angle 2α of the wedge satisfies the equation tan 2α✱ = 2α✱. Such pathological behavior prompted the investigation in this paper of the stresses and displacements that are induced by tractions of O(r−ω) as r→0. The key point is to choose an Airy stress function which generates stresses capable of accommodating unrestricted loading. Fortunately conditions can be derived which pre-determine the form of the necessary Airy stress function. The results show that inhomogeneous boundary conditions can induce stresses of O(r−ω), O(r−ω ln r), or O(r−ω ln2r) as r→0, depending on which conditions are satisfied. The stress function used by Williams is sufficient only if the induced stress and displacement behavior is of the power type. The wedge loaded by uniform antisymmetric shear tractions is shown in this paper to exhibit stresses of O(ln r) as r→0 for the half-plane or crack geometry. At the critical opening angle 2α✱, uniform antisymmetric normal and symmetric shear tractions also induce the above type of stress singularity. No anticipating such stresses, Lévy used an insufficiently general Airy stress function that led to the observed pathological behavior at 2α✱.

The Fracture Toughness of Ice

Topics to be addressed in this paper include the relevance of fracture mechanics to ice engineering the concept of fracture toughness the use of fracture toughness values for ice an examination and assessment of fracture toughness testing to date.

Research trends in ice mechanics

Abstract In sea ice geophysics, the formulation and implementation of a continuum anisotropic ice dynamics model is required in order to increase the spatial resolution of the Polar Ice Prediction System (PIPS) used by the National/Naval Ice Center to provide sea-ice analyses, forecasts, outlooks and ship-routing recommendations within the marginal ice zone of Arctic and Antarctic seas. Currently, too little is known about the formation of leads in the Arctic, a situation that should rapidly improve via automated ice-tracking SAR algorithms. Many questions remain concerning the influences of inhomogeneities (thermal cracks, ridges, thickness variability, and rubble) on wave propagation, constitutive behavior and overall ice strength at various scales. Floe scale ice models appear to offer the means to bridge the scales between geophysical and structural applications by being able to accurately model the mechanics of ridging, rafting and leading. At the scale of ice forces on structures and ships, a diverse range of creep-brittle failure modes awaits incorporation into ice force models. Knowledge concerning the multiaxial compressive failure of freshwater and saline ice is now available. The constitutive modeling of sea ice lags well behind that for freshwater ice. The important issues of scale effects and inhomogeneities on tensile strength at lab- to structural-scale are discussed, as are the links between various scales.

High pressure zone formation during compressive ice failure

Abstract An understanding of the mechanics and physics of the formation of the high pressure zones that form during ice–structure interactions is sought. The influences of time, temperature and scale on the formation of these high pressure zones are explored in this paper. Line-like and localized high pressure contact zones are modeled via elastic-brittle hollow cylinder and hollow sphere idealizations, respectively. For both simultaneous and non-simultaneous contact, the critical lengths of stable cracking that may occur prior to flaking and flexural failure are strongly linked to the current level of specific pressure parameters for both line-like and localized high pressure zones. The stability aspects of the in-plane cracking, and the link between the maximum possible crack lengths and the relative magnitudes of the local and far-field pressures help explain the transitions observed within the realms of ductile, intermittent, and brittle crushing.

Radial cracking with closure

Progressive radial cracking of a clamped plate subjected to crack-face closure is studied. The material behavior is assumed to be elastic-brittle. The cracks are assumed to be relatively long in the sense that the three-dimensional contact problem can be described via a statically equivalent two-dimensional idealization. The number of cracks is supposed large enough to permit a quasi-continuum approach rather than one involving the discussion of discrete sectors. The formulation incorporates the action of both bending and stretching as well as closure effects of the radial crack face contact. Fracture mechanics is used to explore the load-carrying capacity and the importance of the role of the crack-surface-interaction. For a given crack radius, the closure contact width is assumed to be constant. Under this condition, a closed-form solution is obtained for the case of a finite clamped plate subjected to a concentrated force. Crack growth stability considerations predict that the system of radial cracks will initiate and grow unstably over a significant portion of the plate radius. The closure stress distribution is determined exactly in the case of narrow contact widths and approximately otherwise.

Crack propagation and fracture resistance in saline ice

Crack propa gation in saline ice (a model sea ice) is investigated in this study in an atte mpt to under stand the processes of crack growth at one loading rate and two temperatu res. As has been previou sly observed in cold sea ice and warm or cold fresh -water ice, crack growth occurs in initiat ion /arrest incr ement s. The energetic stabil ity cri teria of crack growth are exa mined in saline ice and growth is charact erized in terms of the fractu re-resistance param eter KR. This paper offers the development of a new fractu re geom etry capable of sustained stable crack growth and the prese ntation of fractu re-resis tance curves for saline ice at -25° and -15°C. The important findi ngs of this paper are that: (i) in warm sal ine ice, ext ensive local crack -tip dama ge is acco mpanied by a limited amount of slow, stable crack extension; (ii) fracture in cold saline ice is characte rized by locally negative KR behavior; and (iii) fracture in cold or warm saline ice is cha racterized by glob ally posit ive KR curve behavior.

Ice/metal interfaces: fracture energy and fractography

Results are presented of the fracture tests of ice/metal interfaces in an attempt to utilize fracture mechanics to characterize the failure of ice/solid adhesion. The four-point bending delamination specimen was used to measure the fracture energy of ice/aluminium and ice/steel joints at — 15 °C. The interfacial fracture energy was found to be dependent on ice type and formation procedure of the ice/metal composites. Crack growth was in a manner of asymmetrical bursting, and both cohesive and adhesive failure mechanisms were observed. Although the fracture of ice/metal interfaces was brittle in nature, the evidence of dislocation slip in ice crystals, as revealed by etching and replicating, suggests that microplastic deformations occur in the ice component.

A Lattice Model for Viscoelastic Fracture

A plane, periodic, square-cell lattice is considered,consisting of point particles connected by mass-less viscoelastic bonds.Homogeneous and inhomogeneous problems for steady-state semi-infinitecrack propagation in an unbounded lattice and lattice strip are studied.Expressions for the local-to-global energy-release-rate ratios, stressesand strains of the breaking bonds as well as the crack openingdisplacement are derived. Comparative results are obtained forhomogeneous viscoelastic materials, elastic lattices and homogeneouselastic materials. The influences of viscosity, the discrete structure,cell size, strip width and crack speed on the wave/viscous resistancesto crack propagation are revealed. Some asymptotic results related to animportant asymptotic case of large viscosity (on a scale relative to thelattice cell) are shown. Along with dynamic crack propagation, a theoryfor a slow crack in a viscoelastic lattice is derived.

A Viscoelastic Fictitious Crack Model for the Fracture of Sea Ice

The fracture of sea ice is modeled using a viscoelastic fictitious crack(cohesive zone) model. The sea ice is modeled as a linear viscoelastic material. The fictitious crack model is implemented via the weight function method. The associated stress-separation curve can be rate dependent. The impact of assuming viscoelastic behavior in the bulk as opposed to elastic behavior is studied. Results from the model are compared to the available exact results for various test cases. The model is applied to a large scale in situ sea ice fracture test. Various implications of such applications are pointed out. This viscoelastic fictitious crack model is found to be a promising tool in investigations pertaining to the fracture of sea ice.