Crack tip and associated domain integrals from momentum and energy balance

The assessment of defects in structures of strain hardening material

Given a general balance statement we derive an expression for the associated crack tip flux integral. The conditions under which the integral is physically meaningful and yields a non-trivial result are outlined. To illustrate the approach a number of well known integrals in use in fracture mechanics are derived. It is demonstrated that complementary analogues to these integrals can be derived in a similar fashion and a result indicating the equality of dual integrals under quite general conditions is presented. We discuss the domain integral method as an alternative means of representing crack tip integrals and we show that the method may be interpreted as a particular form of Signorini's theorem of stress means. A discussion of some associated integral identities is presented.

A general treatment of crack tip contour integrals

Solar heat is the acknowledged driving force for climatic change. However, ice sheets are also capable of causing climatic change. This property of ice sheets derives from the facts that ice and rock are crystalline whereas the oceans and atmosphere are fluids and that ice sheets are massive enough to depress the earth's crust well below sea level. These features allow time constants for glacial flow and isostatic compensation to be much larger than those for ocean and atmospheric circulation and therefore somewhat independent of the solar variations that control this circulation. This review examines the nature of dynamic processes in ice streams that give ice sheets their degree of independent behavior and emphasizes the consequences of viscoplastic instability inherent in anisotropic polycrystalline solids such as glacial ice. Viscoplastic instability and subglacial topography are responsible for the formation of ice streams near ice sheet margins grounded below sea level. As a result the West Antarctic marine ice sheet is inherently unstable and can be rapidly carved away by calving bays which migrate up surging ice streams. Analyses of tidal flexure along floating ice stream margins, stress and velocity fields in ice streams, and ice stream boundary conditions are presented and used to interpret ERTS 1 photomosaics for West Antarctica in terms of characteristic ice sheet crevasse patterns that can be used to monitor ice stream surges and to study calving bay dynamics.

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Neil L. Goldman

Papers

Fully plastic crack problems: The center-cracked strip under plane strain