Power-law Theory Research Articles

Creep rates of spray ice

Mars Island, a man-made spray ice island, was constructed in January and February 1986, and was used as a drill platform for petroleum exploration in the Alaskan Beaufort Sea. A series of pressuremeter creep tests was run in the spray ice of Mars Island in March 1986. Individual constant-pressure tests lasted up to 5 days.It is possible to compare the creep behaviour of the spray ice as interpreted from the pressuremeter tests with the creep behaviour interpreted from the island settlement records. These comparisons are made for both primary and secondary creep on the basis of conventional power law theory. The following points are of particular interest: (1) The primary creep data can be characterized using a simple power law. The exponent of time for spray ice is similar to that for solid polycrystalline ice. The exponent of stress is different for the two kinds of ice. (2) Pressuremeter tests gave secondary creep information that correlates well with the steady-rate settlement of the island. (3) Research into the possible range of primary creep parameters for spray ice is required, given that primary creep accounted for a large portion of the settlement of Mars Island. In particular, the effect of ice density on creep rates mast be resolved. (4) The pressuremeter is potentially an excellent design control device during the manufacture of future spray ice islands. The results of constant-pressure tests of 1–2 days duration could be used to check the design assumptions pertaining to the expected consolidation of the ice mass with time. Key words: spray ice, creep, artificial islands, pressuremeter, settlement.

Combined Loading of a Fully Plastic Ligament Ahead of an Edge-Crack

Complete, accurate numerical results are given for the solution to the problem of a semi-infinite crack aligned perpendicularly to the free-edge of a semi-infinite half space in which the ligament is subject to arbitrary combinations of bending and tension or compression. The material is an incompressible, pure power-law deformation theory solid. Conditions of plane strain are assumed. Approximate solutions are proposed for predominantly bending loadings and also for predominantly stretching loadings.

Aspects of the Calendering of Plastics Compositions

Pressure distribution curves derived from isothermal power-law theory are shown to match closely with the experimental data of Bergen and Scott. A method of estimating roll bearing loads from torque measurements obviates errors incurred when using plastometry. An analysis of unequal roll speed calendering is presented and surface pattern formation is explained as a laminar flow effect, with experimental evidence.

Application of Karman's Logarithmic Law to Prediction of Airship Hull Drag

A F T E R experiments had shown that the i power law theory of von Karman and Prandtl, for the skin friction of a pointed flat plate in a two-dimensional flow parallel to the surface and perpendicular to the leading edge, could be used satisfactorily in determining the skin friction at the curved surface of a streamline body in a two-dimensional flow when the radius of curvature is large compared to the boundary layer thickness, Jones, Dryden and Kuethe extended the theory so as to give an account of the skin friction acting on a dirigible model in an axial flow. In both these discussions the dirigible was replaced by an ''equivalent flat plate. ' ' Although Boltze had given the equations for the laminar boundary layer for a body with axial symmetry about an axis in the direction of flow, and Levi-Civita had attacked the general problem of the turbulent boundary layer for a body of any shape, it remained for Millikan to give a satisfactory analysis applicable to dirigible models. Millikan derived the approximate form of the boundary layer equations in the neighborhood of the surface of a figure of revolution from the Navier-Stokes and continuity equations for the steady motion of a viscous incompressible fluid, letting the kinematic viscosity go to zero and neglecting powers of the square root of the kinematic viscosity higher than the first. The resulting equations are valid when the boundary layer thickness is small compared to its distance from the axis. In the turbulent boundary layer, Millikan assumed the one-seventh power law for the velocity profile. However, von Karman has shown that the power law is merely an interpolation of or approximation to the logarithmic law; and experiments, especially those of Nikuradse, show that the l /7 th power does indeed become a l /8 th power, then a l /9 th power, etc., as the Reynolds' Number increases. Both Millikan and von Karman have pointed out the desirability, where the analysis is to be used to predict drag coefficients at large Reynolds' Numbers, of extending Millikan's work by introduction of the logarithmic law. As a preliminary step, Millikan's equations were generalised to hold for a 1/n-th power law for the velocity distribution, and drag coefficients were calculated for several values of n for the N. P. L. Long Model at a large Reynolds' Number. The differences in the drag coefficients for the various power laws were found to be sufficient to justify the further refinement of introducing the logarithmic law. It was then assumed that the logarithmic velocity distribution, as developed by von Karman for the boundary layer on the flat plate, holds also for the boundary layer on the axially symmetric body. Aqcordingly we introduce the logarithmic velocity distribution