Experimental compliance calibration of the NASA Lewis Research Center Mode 2 fatigue specimen

Calibration of the mode II aluminum fatigue specimen was performed experimentally to provide displacement and stress intensity coefficients over crack length to specimen width ratios (a/W) of 0.5 to 0.9. Displacements were measured both at the specimen notch mouth and at the intersection of the notch with the centerline of the loading pin holes

Effect of long-time, elevated-temperature exposures to vacuum and lithium on the properties of a tantalum alloy, T-111

The effect of long-term, elevated-temperature vacuum and lithium exposures on the mechanical properties of T-111 (Ta-8W-2Hf) is determined. Exposure conditions were for 1000 hours at 980 or 1315 C, 5000 hours at 1315 C, and a duplex temperature exposure of 1000 hours at 980 C plus 4000 hours at 1040 C. The exposures resulted in reduced tensile and creep strengths of the T-111 in the 900 to 1100 C temperature range where a dynamic strain-age-strengthening mechanism is operative in this alloy. This strength reduction was attributed to the depletion of oxygen from solid solution in this alloy

Load-displacement measurement and work determination in three-point bend tests of notched or precracked specimens

Suggestions for testing of notched or cracked three-point bend specimens are presented which: (1) correct displacement measurement errors resulting from misalignment between the load applicator and specimen; (2) account for coincidental strains not associated with the work of crack extension; (3) simplify record analysis and processing; and (4) extend displacement gage range without sacrifice of sensitivity or accuracy. These testing details are particularly applicable to procedures in which the crack extension force is determined from the work done on the specimen

Comparison tests and experimental compliance calibration of the proposed standard round compact plane strain fracture toughness specimen

Standard round specimen fracture test results compared satisfactorily with results from standard rectangular compact specimens machined from the same material. The location of the loading pin holes was found to provide adequate strength in the load bearing region for plane strain fracture toughness testing. Excellent agreement was found between the stress intensity coefficient values obtained from compliance measurements and the analytic solution proposed for inclusion in the standard test method. Load displacement measurements were made using long armed displacement gages and hollow loading cylinders. Gage points registered on the loading hole surfaces through small holes in the walls of the loading cylinders

Mode 2 fatigue crack growth specimen development

A Mode II test specimen was developed which has potential application in understanding phemonena associated with mixed mode fatigue failures in high performance aircraft engine bearing races. The attributes of the specimen are: it contains one single ended notch, which simplifiers data gathering and reduction; the fatigue crack grous in-line with the direction of load application; a single axis test machine is sufficient to perform testing; and the Mode I component is vanishingly small

Monitoring crack extension in fracture toughness tests by ultrasonics

An ultrasonic method was used to observe the onset of crack extension and to monitor continued crack growth in fracture toughness specimens during three point bend tests. A 20 MHz transducer was used with commercially available equipment to detect average crack extension less than 0.09 mm. The material tested was a 300-grade maraging steel in the annealed condition. A crack extension resistance curve was developed to demonstrate the usefulness of the ultrasonic method for minimizing the number of tests required to generate such curves

A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

An interpolation theorem for proper holomorphic embeddings

Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and a discrete sequence b_j in C^m where m > [3n/2], there exists a proper holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,.... This is the interpolation version of the embedding theorem due to Eliashberg, Gromov and Schurmann. The dimension m cannot be lowered in general due to an example of Forster

A mathematical model of melt lake development on an ice shelf

The accumulation of surface meltwater on ice shelves can lead to the formation of melt lakes. Melt lakes have been implicated in ice shelf collapse; Antarctica's Larsen B Ice Shelf was observed to have a large amount of surface melt lakes present preceding its collapse in 2002. Such collapse can affect ocean circulation and temperature, cause habitat loss and contribute to sea level rise through the acceleration of tributary glaciers. We present a mathematical model of a surface melt lake on an idealised ice shelf. The model incorporates a calculation of the ice shelf surface energy balance, heat transfer through the firn, the production and percolation of meltwater into the firn, the formation of ice lenses and the development and refreezing of surface melt lakes. The model is applied to the Larsen C Ice Shelf, where melt lakes have been observed. This region has warmed several times the global average over the last century and the Larsen C firn layer could become saturated with meltwater by the end of the century. When forced with weather station data, our model produces surface melting, meltwater accumulation, and melt lake development consistent with observations. We examine the sensitivity of lake formation to uncertain parameters, and provide evidence of the importance of processes such as lateral meltwater transport. We conclude that melt lakes impact surface melt and firn density and warrant inclusion in dynamic-thermodynamic models of ice shelf evolution within climate models, of which our model could form the basis for the thermodynamic component

An embedding of ℂ in ℂ 2 with hyperbolic complement

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46249/1/208_2005_Article_BF01445264.pd